Religions > Atheism > OT: What is the smallest number that can be written as the sum of two cubes in two different ways
| Topic: |
Religions > Atheism |
| User: |
"maff" |
| Date: |
24 Feb 2005 04:21:06 AM |
| Object: |
OT: What is the smallest number that can be written as the sum of two cubes in two different ways |
What is the smallest number that can be written as the sum of two cubes
in two different ways?
Srinivasa Ramanujan
http://groups-beta.google.com/group/talk.origins/msg/7889bb6a3abc4836
Math OR Maths OR Mathematics OR Mathematical OR Mathematician OR
Mathematicians
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OT: Some numbers you can't count on
http://tinyurl.com/ysjn
A Blueprint for the Future
http://snipurl.com/a684
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| User: "" |
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| Title: Re: OT: What is the smallest number that can be written as the sum of two cubes in two different ways |
24 Feb 2005 10:03:30 AM |
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If -1 is considered smaller than 0, then this question degenerates to
asking
what is the largest negative number that 2 cubes can produce. And it is
a
very large negative number indeed.
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| User: "Al Klein" |
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| Title: Re: OT: What is the smallest number that can be written as the sum of two cubes in two different ways |
24 Feb 2005 03:39:06 PM |
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On 24 Feb 2005 08:03:30 -0800, said in alt.atheism:
If -1 is considered smaller than 0, then this question degenerates to
asking
what is the largest negative number that 2 cubes can produce. And it is a
very large negative number indeed.
So large, in fact, that there is no such number.
--
rukbat at verizon dot net
I cannot conceive of a god who rewards and punishes his creatures
or has a will of the kind that we experience in ourselves. Neither
can I nor would I want to conceive of an individual that survives
its physical death; let feeble souls, from fear or absurd egotism,
cherish such thoughts. I am satisfied with the mystery of the eter-
nity of life and a glimpse of the marvelous structure of the exist-
ing world, together with the devoted striving to comprehend a
portion, be it ever so tiny, of the Reason that manifests itself in
nature.
- Albert Einstein, as quoted in _Billions and Billions_, Carl Sagan.
(random sig, produced by SigChanger)
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| User: "kevin hollingworth" |
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| Title: Re: OT: What is the smallest number that can be written as the sum of two cubes in two different ways |
24 Feb 2005 03:57:34 PM |
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"Al Klein" <rukbat@pern.invalid> wrote in message
news:pais11tueggjb44td2kt1lnq32ehhep13h@4ax.com...
On 24 Feb 2005 08:03:30 -0800, said in alt.atheism:
If -1 is considered smaller than 0, then this question degenerates to
asking
what is the largest negative number that 2 cubes can produce. And it is a
very large negative number indeed.
So large, in fact, that there is no such number.
--
rukbat at verizon dot net
I cannot conceive of a god who rewards and punishes his creatures
or has a will of the kind that we experience in ourselves. Neither
can I nor would I want to conceive of an individual that survives
its physical death; let feeble souls, from fear or absurd egotism,
cherish such thoughts. I am satisfied with the mystery of the eter-
nity of life and a glimpse of the marvelous structure of the exist-
ing world, together with the devoted striving to comprehend a
portion, be it ever so tiny, of the Reason that manifests itself in
nature.
- Albert Einstein, as quoted in _Billions and Billions_, Carl Sagan.
(random sig, produced by SigChanger)
-Albert Einstein, a man with more than one blunder!!!
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| User: "Bobby D. Bryant" |
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| Title: Re: OT: What is the smallest number that can be written as the sum of two cubes in two different ways |
24 Feb 2005 04:41:18 AM |
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On Thu, 24 Feb 2005, "maff" <maff91@yahoo.com> wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
Yeah, that question has been bothering me lately.
--
Bobby Bryant
Austin, Texas
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| User: "Mark VandeWettering" |
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| Title: Re: OT: What is the smallest number that can be written as the sum of two cubes in two different ways |
24 Feb 2005 03:05:54 PM |
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["Followup-To:" header set to talk.origins.]
On 2005-02-24, maff <maff91@yahoo.com> wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
That would be 1729, wouldn't it?
10^3 + 9^3 = 1729
12^3 + 1^3 = 1729
It was also the number of the taxi that brought me here. Strange..
Mark
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| User: "maff" |
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| Title: Re: OT: What is the smallest number that can be written as the sum of two cubes in two different ways |
25 Feb 2005 06:11:50 AM |
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maff wrote:
What is the smallest number that can be written as the sum of two
cubes
in two different ways?
Srinivasa Ramanujan
http://groups-beta.google.com/group/talk.origins/msg/7889bb6a3abc4836
Godfrey Hardy
http://groups-beta.google.com/group/talk.origins/msg/3cbfea2e3936ec69
Math OR Maths OR Mathematics OR Mathematical OR Mathematician OR
Mathematicians
http://news.google.com/news?q=%20Math%20OR%20Maths%20OR%20Mathematics%20OR%20Mathematical%20OR%20Mathematician%20OR%20Mathematicians&num=100&hl=en&lr=&ie=UTF-8&sa=N&tab=gn
http://www.google.com/search?q=Math+OR+Maths+OR+Mathematics+OR+Mathematical+OR+Mathematician+OR+Mathematicians&num=100&hl=en&lr=&ie=UTF-8&tab=nw&sa=N
http://www.google.com/search?q=Math+OR+Maths+OR+Mathematics+OR+Mathematical+OR+Mathematician+OR+Mathematicians&num=100&hl=en&lr=&ie=UTF-8&output=search&cat=gwd/Top
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OT: Some numbers you can't count on
http://tinyurl.com/ysjn
A Blueprint for the Future
http://snipurl.com/a684
.
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| User: "dkomo" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
24 Feb 2005 12:14:05 PM |
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maff wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
That's obvious, it's 1729 = 1^3 + 12^3 = 9^3 + 10^3.
1729 is also known as Taxicab(2) where Taxicab(n) is the smallest number
expressible as the sum of two cubes in n different ways.
Taxicab(3) = 87539319 = 167^3 + 436^3 = 228^3 + 423^3 = 255^3 + 414^3
Taxicab(4) = 6963472309248 = 2421^3 + 19083^3 = 5436^3 + 18948^3 =
10200^3 + 18072^3 = 13322^3 + 16630^3
The largest known Taxicab is Taxicab(5), which I won't bother to write
down, leaving it as an exercise for the reader.
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| User: "Secular Fundamentalist" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
24 Feb 2005 04:55:37 AM |
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maff wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
9: 8+1; 1+8.
--
David Silverman F.L.A.H.N.
aa #2208
Ignorance is death.
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| User: "Moremix" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
24 Feb 2005 11:31:24 PM |
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"Secular Fundamentalist" <moc.turtle@eltrut.com> wrote in message
news:yY-dnQ4FiII-L4DfRVnyhA@brightview.com...
maff wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
9: 8+1; 1+8.
--
David Silverman F.L.A.H.N.
aa #2208
Ignorance is death.
Would it not be 1??
0 cubed =0
1 cubed=1
0+1=1 1+0=1
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| User: "Dubh Ghall" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
24 Feb 2005 08:06:52 AM |
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On Thu, 24 Feb 2005 10:55:37 +0000, Secular Fundamentalist
<moc.turtle@eltrut.com> wrote:
maff wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
9: 8+1; 1+8.
2. 1+1, and 2.
--
Puck Greenman
The spelling Like any opinion stated here
purely my own
#162 BAAWA Knight.
Plonked by Rob Duncan
January 27th
Na bister 500,000
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| User: "Pithecanthropus Erectus" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwo cubes in two different ways |
24 Feb 2005 11:59:28 AM |
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Dubh Ghall wrote:
On Thu, 24 Feb 2005 10:55:37 +0000, Secular Fundamentalist
<moc.turtle@eltrut.com> wrote:
maff wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
9: 8+1; 1+8.
2. 1+1, and 2.
Remind me. What is the cube root of 2? Is it a whole number. I didn't
think so.
Although, the puzzle didn't specify that the answer needs to be the cube
of an integer....
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| User: "Dubh Ghall" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwo cubes in two different ways |
24 Feb 2005 05:35:04 PM |
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On Thu, 24 Feb 2005 11:59:28 -0600, Pithecanthropus Erectus
<tuibguy1SPAMAJAM@comcast.net> wrote:
Dubh Ghall wrote:
On Thu, 24 Feb 2005 10:55:37 +0000, Secular Fundamentalist
<moc.turtle@eltrut.com> wrote:
maff wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
9: 8+1; 1+8.
2. 1+1, and 2.
Remind me. What is the cube root of 2?
1.2599210499
Is it a whole number.
The question didn't say, "whole number".
I didn't think so.
Although, the puzzle didn't specify that the answer needs to be the cube
of an integer....
Just so: And if it aint expressly forbidden, then AFAIAC, it is allowed. (:-)
--
Puck Greenman
The spelling Like any opinion stated here
purely my own
#162 BAAWA Knight.
Plonked by Rob Duncan
January 27th
Na bister 500,000
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| User: "Secular Fundamentalist" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
24 Feb 2005 04:57:26 AM |
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maff wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
Sorry, got that wrong. It's 1.
--
David Silverman F.L.A.H.N.
aa #2208
Ignorance is death.
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| User: "Féachadóir" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
24 Feb 2005 06:10:43 AM |
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Scríobh Secular Fundamentalist <moc.turtle@eltrut.com>:
maff wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's zero.
--
"Ná sáruigther Seinglenn
aitreb na lec nime"
© Féachadóir
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| User: "Secular Fundamentalist" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwo cubes in two different ways |
24 Feb 2005 06:40:26 AM |
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Féachadóir wrote:
Scríobh Secular Fundamentalist <moc.turtle@eltrut.com>:
maff wrote:
What is the smallest number that can be written as the sum of two cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's zero.
That can't be *written* in two different ways.
--
David Silverman F.L.A.H.N.
aa #2208
Ignorance is death.
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| User: "maff" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
24 Feb 2005 06:27:14 AM |
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Féachadóir wrote:
Scríobh Secular Fundamentalist <moc.turtle@eltrut.com>:
maff wrote:
What is the smallest number that can be written as the sum of two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's zero.
Don't be stupid. Have you read the question?
--
"Ná sáruigther Seinglenn
aitreb na lec nime"
© Féachadóir
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| User: "Richard Harter" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
24 Feb 2005 10:41:08 AM |
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On 24 Feb 2005 04:27:14 -0800, "maff" <maff91@yahoo.com> wrote:
Féachadóir wrote:
Scríobh Secular Fundamentalist <moc.turtle@eltrut.com>:
maff wrote:
What is the smallest number that can be written as the sum of two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's zero.
Don't be stupid. Have you read the question?
Perhaps you should read the question that you asked, not the one you
thought you were asking.
BTW: Not only is this OT it is cross-posted. Why is that?
Richard Harter,
http://home.tiac.net/~cri, http://www.varinoma.com
All my life I wanted to be someone;
I guess I should have been more specific.
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| User: "" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
24 Feb 2005 11:22:33 AM |
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Richard Harter wrote:
On 24 Feb 2005 04:27:14 -0800, "maff" <maff91@yahoo.com> wrote:
Féachadóir wrote:
Scríobh Secular Fundamentalist <moc.turtle@eltrut.com>:
maff wrote:
What is the smallest number that can be written as the sum of
two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's zero.
Don't be stupid. Have you read the question?
Perhaps you should read the question that you asked, not the one you
thought you were asking.
Fallacy of Literalism. Far too common in alt.atheism.
(0^3 + 0^3 = 1^3 + (-1)^3 = 0) is obviously not an intended answer to
the question. Heck, to be entirely literal, the question doesn't even
specify integers, and there is no smallest real expressible as the sum
of cubes of two reals in two different ways. Every real is expressible
as the sum of cubes of two reals in an infinity of ways. So the
question itself is invalid, a trick? Not at all. (Although many
alt.atheists have tried the same fallacious technique
(hyper-literalism, of a translated text no less) in a laughable attempt
to "invalidate" the Bible and thereby Christianity.)
What is the smallest integer n such that there exist 4 different
non-negative integers a, b, c, d, such that a^3 + b^3 = c^3 + d^3 = n?
I'm not sure "non-negative" is intended, but this is obviously closer
to the intent of the original question.
Jeff
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| User: "Richard Harter" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
25 Feb 2005 03:35:54 AM |
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On 24 Feb 2005 09:22:33 -0800, wrote:
Richard Harter wrote:
On 24 Feb 2005 04:27:14 -0800, "maff" <maff91@yahoo.com> wrote:
Féachadóir wrote:
Scríobh Secular Fundamentalist <moc.turtle@eltrut.com>:
maff wrote:
What is the smallest number that can be written as the sum of
two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's zero.
Don't be stupid. Have you read the question?
Perhaps you should read the question that you asked, not the one you
thought you were asking.
Fallacy of Literalism. Far too common in alt.atheism.
Bosh. Literalism is not a fallacy; it may be annoying and not to the
purpose, but it is not a fallacy.
Be that as it may, your comment is irrelevant. It is clear that the
person whom maff was addressing was trading on the lack of precision
in the question. Maff's comment was not only rude, it was obtuse.
Your comment was not rude.
Richard Harter,
http://home.tiac.net/~cri, http://www.varinoma.com
All my life I wanted to be someone;
I guess I should have been more specific.
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| User: "" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
25 Feb 2005 11:18:34 AM |
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Richard Harter wrote:
On 24 Feb 2005 09:22:33 -0800, wrote:
Richard Harter wrote:
On 24 Feb 2005 04:27:14 -0800, "maff" <maff91@yahoo.com> wrote:
Féachadóir wrote:
Scríobh Secular Fundamentalist <moc.turtle@eltrut.com>:
maff wrote:
What is the smallest number that can be written as the sum
of
two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's zero.
Don't be stupid. Have you read the question?
Perhaps you should read the question that you asked, not the one
you
thought you were asking.
Fallacy of Literalism. Far too common in alt.atheism.
Bosh. Literalism is not a fallacy; it may be annoying and not to the
purpose, but it is not a fallacy.
It is a sub-category of the Strawman Fallacy. If the question is
imprecise, it is fallacious to presume any one interpretation,
including a literal one, and insist that that interpretation is the
intention of the author. Maff, as the author, is the one who makes
that call; if your literalism is "annoying" to Maff (i.e. not the way
_he_ intended the question to be interpreted), you are committing a
Strawman Fallacy. (OTOH, it is certainly kosher to point out that the
question is imprecise and then give a literal interpretation as an
_example_ of why.)
Jeff
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| User: "Richard Harter" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
27 Feb 2005 11:57:18 AM |
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On 25 Feb 2005 09:18:34 -0800, wrote:
Richard Harter wrote:
On 24 Feb 2005 09:22:33 -0800, wrote:
Richard Harter wrote:
On 24 Feb 2005 04:27:14 -0800, "maff" <maff91@yahoo.com> wrote:
Féachadóir wrote:
Scríobh Secular Fundamentalist <moc.turtle@eltrut.com>:
maff wrote:
What is the smallest number that can be written as the sum
of
two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's zero.
Don't be stupid. Have you read the question?
Perhaps you should read the question that you asked, not the one
you
thought you were asking.
Fallacy of Literalism. Far too common in alt.atheism.
Bosh. Literalism is not a fallacy; it may be annoying and not to the
purpose, but it is not a fallacy.
It is a sub-category of the Strawman Fallacy. If the question is
imprecise, it is fallacious to presume any one interpretation,
including a literal one, and insist that that interpretation is the
intention of the author. Maff, as the author, is the one who makes
that call; if your literalism is "annoying" to Maff (i.e. not the way
_he_ intended the question to be interpreted), you are committing a
Strawman Fallacy. (OTOH, it is certainly kosher to point out that the
question is imprecise and then give a literal interpretation as an
_example_ of why.)
I opine that you are a little confused about what is meant by a
fallacy, and rather antiquated (to say nothing of being hopelessly
provincial and dogmatic) in your notions of interpretation. Be that
as it may, I am confident that you are the best of all good fellows,
and that your mother loves you dearly.
Richard Harter,
http://home.tiac.net/~cri, http://www.varinoma.com
All my life I wanted to be someone;
I guess I should have been more specific.
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| User: "John Harshman" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwo cubes in two different ways |
24 Feb 2005 11:03:24 AM |
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maff wrote:
Féachadóir wrote:
Scríobh Secular Fundamentalist <moc.turtle@eltrut.com>:
maff wrote:
What is the smallest number that can be written as the sum of two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's zero.
Don't be stupid. Have you read the question?
I think you're having a little definitional problem. You forgot to
specify that the numbers must all be natural numbers. If we allow
negative integers, there is no smallest number. If we allow positive
irrational numbers, ditto, but at least zero is a bound.
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| User: "maff" |
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| Title: Re: OT: What is the smallest number that can be written as the sumof two cubes in two different ways |
24 Feb 2005 05:20:14 AM |
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Secular Fundamentalist wrote:
maff wrote:
What is the smallest number that can be written as the sum of two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's only one way. It should be done in two different ways.
--
David Silverman F.L.A.H.N.
aa #2208
Ignorance is death.
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| User: "Secular Fundamentalist" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwo cubes in two different ways |
24 Feb 2005 06:39:03 AM |
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maff wrote:
Secular Fundamentalist wrote:
maff wrote:
What is the smallest number that can be written as the sum of two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's only one way. It should be done in two different ways.
Oh! *done* in 2 different ways. i.e. the sum of 2 different pairs of cubes.
91.
--
David Silverman F.L.A.H.N.
aa #2208
Ignorance is death.
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| User: "maff" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwo cubes in two different ways |
24 Feb 2005 02:11:48 PM |
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Secular Fundamentalist wrote:
maff wrote:
Secular Fundamentalist wrote:
maff wrote:
What is the smallest number that can be written as the sum of two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's only one way. It should be done in two different ways.
Oh! *done* in 2 different ways. i.e. the sum of 2 different pairs of
cubes.
91.
Nope.
a(exp.3) + b(exp.3) = c(exp.3) + d(exp.3) = x
--
David Silverman F.L.A.H.N.
aa #2208
Ignorance is death.
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| User: "Secular Fundamentalist" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwocubes in two different ways |
24 Feb 2005 04:11:26 PM |
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maff wrote:
Secular Fundamentalist wrote:
maff wrote:
Secular Fundamentalist wrote:
maff wrote:
What is the smallest number that can be written as the sum of two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's only one way. It should be done in two different ways.
Oh! *done* in 2 different ways. i.e. the sum of 2 different pairs of
cubes.
91.
Nope.
a(exp.3) + b(exp.3) = c(exp.3) + d(exp.3) = x
a=6,b=-5,c=4,d=3 x=91
--
David Silverman F.L.A.H.N.
aa #2208
Ignorance is death.
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| User: "maff" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwocubes in two different ways |
25 Feb 2005 03:53:39 AM |
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Secular Fundamentalist wrote:
maff wrote:
Secular Fundamentalist wrote:
maff wrote:
Secular Fundamentalist wrote:
maff wrote:
What is the smallest number that can be written as the sum of
two
cubes
in two different ways?
Sorry, got that wrong. It's 1.
It's only one way. It should be done in two different ways.
Oh! *done* in 2 different ways. i.e. the sum of 2 different pairs
of
cubes.
91.
Nope.
a(exp.3) + b(exp.3) = c(exp.3) + d(exp.3) = x
a=6,b=-5,c=4,d=3 x=91
Cubes are always positive.
--
David Silverman F.L.A.H.N.
aa #2208
Ignorance is death.
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| User: "Secular Fundamentalist" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwocubesin two different ways |
25 Feb 2005 05:13:04 AM |
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maff wrote:
Cubes are always positive.
Surely -x(-x) = x^2, -x(x^2) = -x^3? Otherwise, the product of two
numbers would always be positive.
--
David Silverman F.L.A.H.N.
aa #2208
We are witnessing the collapse of intellect. Blame rests with a failure
to roundly repudiate existentialism.
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| User: "maff" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwocubesin two different ways |
25 Feb 2005 05:44:01 AM |
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Secular Fundamentalist wrote:
maff wrote:
Cubes are always positive.
Surely -x(-x) = x^2, -x(x^2) = -x^3? Otherwise, the product of two
numbers would always be positive.
It has to be postive for you to find the smallest number. Taxicabs
don't have negative values.
--
David Silverman F.L.A.H.N.
aa #2208
We are witnessing the collapse of intellect. Blame rests with a
failure
to roundly repudiate existentialism.
.
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| User: "maff" |
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| Title: Re: OT: What is the smallest number that can be written as the sumoftwocubesin two different ways |
27 Feb 2005 07:00:01 AM |
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Secular Fundamentalist wrote:
maff wrote:
Cubes are always positive.
Surely -x(-x) = x^2, -x(x^2) = -x^3? Otherwise, the product of two
numbers would always be positive.
Once you take negative integers then the smallest will be minus
infinity. It won't be 91.
--
David Silverman F.L.A.H.N.
aa #2208
We are witnessing the collapse of intellect. Blame rests with a
failure
to roundly repudiate existentialism.
.
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