# Fermat's last theorem — Google and PCMag.com

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. – The Chaz 2.0 Aug 17 '11 at 15:07
There is a good deal of uncertainty about the year Fermat was born. – André Nicolas Aug 17 '11 at 15:09
Kudos for @oosterwal 's choice of an appropriate tag dripping with delicious irony. – Willie Wong Aug 17 '11 at 15:57
Even the portrait is incorrect - it is Kepler, not Fermat. That's worse than the Legendre portrait fiasco. – Bill Dubuque Aug 17 '11 at 16:12
Which portrait? The one at pcmag.com/article2/0,2817,2391245,00.asp now is the same as in Wikipedia en.wikipedia.org/wiki/File:Pierre_de_Fermat.jpg: maybe it has been changed. However, I found a Kepler portrait labelled as Fermat at news.m3n4.com/general/2011/pierre-de-fermat – Robert Israel Aug 17 '11 at 20:48

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 – Bonanza Aug 17 '11 at 15:04
trollface didn't render correctly. Maybe you need $trollface$ :) – The Chaz 2.0 Aug 17 '11 at 15:06
I fixed the post. – gereeter Aug 17 '11 at 15:14

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.

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