Fermat's last theorem -- Google and PCMag.com

Solution 1:

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.

Solution 2:

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).

Solution 3:

The theorem should read,

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