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In recognition of Fermat's 410th birthday, Google ha(s/d) a special google-doodle with Fermat's last theorem.

The first link point(s/ed) to an article on PCMag.com which states:

In time, Fermat was considered to be the founder of the modern number theory. He came up with Fermat's Last Theorem, which states that $x^n + y^n = z^n$.

Am I missing something or is the PCMag article missing something?

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    The article is missing something.2011-08-17
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    There is a good deal of uncertainty about the year Fermat was born.2011-08-17
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    Kudos for @oosterwal 's choice of an appropriate tag dripping with delicious irony.2011-08-17
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    Even the portrait is incorrect - it is Kepler, not Fermat. That's worse than the [Legendre portrait fiasco.](http://www.ams.org/notices/200911/rtx091101440p.pdf)2011-08-17
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    Which portrait? The one at http://www.pcmag.com/article2/0,2817,2391245,00.asp now is the same as in Wikipedia http://en.wikipedia.org/wiki/File:Pierre_de_Fermat.jpg: maybe it has been changed. However, I found a Kepler portrait labelled as Fermat at http://news.m3n4.com/general/2011/pierre-de-fermat2011-08-17
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    @Robert: See the comments in the article. It was changed.2011-08-17

3 Answers 3

5

The theorem should read,

There do not exist nonzero integers $x, y, z$ such that $x^n+y^n=z^n$ for any $n>2$.

19

PCMag's unreliability does not end there. Later on in the same short article we have

"He died in the belief that he had found a relation which every prime must satisfy, namely $2^{2n}+1= \:\text{a prime}.$"

Then the article tells us that Euler disproved this by showing it was false at $n=5$. Quite an achievement for Euler, showing that $1025$ is not prime!

Of course it should be $2^{2^n}+1$, not $2^{2n}+1$.

Also, "that every prime must satisfy" is wonderfully ambiguous.

8

PCMag is missing something. Fermat's Last Theorem is that for integers $x$, $y$, $z$, and $n$, with $n > 2$, $x^n + y^n \ne z^n$ (provided that $x$, $y$, and $z$ are nonzero).

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    ..provided $xyz\neq 0$. *trollface*2011-08-17
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    *trollface* didn't render correctly. Maybe you need $trollface$ :)2011-08-17
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    I fixed the post.2011-08-17