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jmorriss@idirect.com
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 Posted: Thu Jul 03, 2008 6:50 am Post subject: Almost a Fermat Counterexample? |
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Is there any collection of examples that <<almost>> disprove Fermat's
last Theorem?
In other words:
Has anyone studied integers a, b, c, n, and e, such that
a^n + b^n = c^n + e, where a, b, c are positive, n > 2, and abs(e) is
really small, compared to a, b, and c? |
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hagman
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| Posted: Thu Jul 03, 2008 8:43 am Post subject: Re: Almost a Fermat Counterexample? |
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On 3 Jul., 08:50, "jmorr...@idirect.com" <jmorr...@idirect.com> wrote:
| Quote: |
Is there any collection of examples that <<almost>> disprove Fermat's
last Theorem?
In other words:
Has anyone studied integers a, b, c, n, and e, such that
a^n + b^n = c^n + e, where a, b, c are positive, n > 2, and abs(e) is
really small, compared to a, b, and c?
|
Hello, taxi!
10^3 + 9^3 = 12^3 + 1
hagman |
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jmorriss@idirect.com
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| Posted: Fri Jul 04, 2008 2:44 am Post subject: Re: Almost a Fermat Counterexample? |
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On Jul 3, 2:50 am, "jmorr...@idirect.com" <jmorr...@idirect.com>
wrote:
| Quote: |
Is there any collection of examples that <<almost>> disprove Fermat's
last Theorem?
In other words:
Has anyone studied integers a, b, c, n, and e, such that
a^n + b^n = c^n + e, where a, b, c are positive, n > 2, and abs(e) is
really small, compared to a, b, and c?
|
Sorry, I was not too clear... I was thinking of examples along the
lines of (courtesy of "The Simpsons"):
3987 ^ 12 + 4365 ^ 12 = 4472 ^ 12 with an error of less than 2 *
10^-11 |
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Guest
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| Posted: Fri Jul 04, 2008 8:25 am Post subject: Re: Almost a Fermat Counterexample? |
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On Jul 4, 2:37 pm, Gerry Myerson <ge...@maths.mq.edi.ai.i2u4email>
wrote:
| Quote: |
In article
05b62d01-4456-4d7c-878d-77e192ba1...@f36g2000hsa.googlegroups.com>,
"jmorr...@idirect.com" <jmorr...@idirect.com> wrote:
On Jul 3, 2:50 am, "jmorr...@idirect.com" <jmorr...@idirect.com
wrote:
Is there any collection of examples that <<almost>> disprove Fermat's
last Theorem?
In other words:
Has anyone studied integers a, b, c, n, and e, such that
a^n + b^n = c^n + e, where a, b, c are positive, n > 2, and abs(e) is
really small, compared to a, b, and c?
Sorry, I was not too clear... I was thinking of examples along the
lines of (courtesy of "The Simpsons"):
3987 ^ 12 + 4365 ^ 12 = 4472 ^ 12 with an error of less than 2 *
10^-11
http://www.math.harvard.edu/~elkies/ferm.html
Tables of Fermat ``near-misses'':
approximate solutions of x^n + y^n = z^n
in integers with 0 < x <= y < z < 223 and n in [4,20]
There was once an April Fool's hoax around many maths depts claiming |
that Noam Elkies had found a counterexample to the Fermat theorem. I
wonder if the triplet cited in that hoax was such a near miss. (Not
sure if Elkies had anything to do with the hoax or not.)
Paul Epstein |
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Gerry Myerson
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| Posted: Fri Jul 04, 2008 11:02 am Post subject: Re: Almost a Fermat Counterexample? |
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In article
<05b62d01-4456-4d7c-878d-77e192ba112c@f36g2000hsa.googlegroups.com>,
"jmorriss@idirect.com" <jmorriss@idirect.com> wrote:
| Quote: |
On Jul 3, 2:50 am, "jmorr...@idirect.com" <jmorr...@idirect.com
wrote:
Is there any collection of examples that <<almost>> disprove Fermat's
last Theorem?
In other words:
Has anyone studied integers a, b, c, n, and e, such that
a^n + b^n = c^n + e, where a, b, c are positive, n > 2, and abs(e) is
really small, compared to a, b, and c?
Sorry, I was not too clear... I was thinking of examples along the
lines of (courtesy of "The Simpsons"):
3987 ^ 12 + 4365 ^ 12 = 4472 ^ 12 with an error of less than 2 *
10^-11
|
http://www.math.harvard.edu/~elkies/ferm.html
Tables of Fermat ``near-misses'':
approximate solutions of x^n + y^n = z^n
in integers with 0 < x <= y < z < 223 and n in [4,20]
--
Gerry Myerson (gerry@maths.mq.edi.ai) (i -> u for email) |
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