3^x + 4^y equals 5^z has Unique Solution/Mistake

Source Work

 * The Dictionary
 * $2$
 * $2$

Mistake

 * Also, the only solution of $3^x + 4^y = 5^z$ in integers is $x = y = z = 2$. The equation $5^x + 12^y = 13^z$ has the same unique solution.

Correction
What it should say is:


 * Also, the only solution of $3^x + 4^y = 5^z$ in (strictly) positive integers is $x = y = z = 2$ ...

as we also have the solutions:

In the original work from which Wells's information was taken, the correct specification for $x$, $y$ and $z$ was used.

This factoid was not included in the first edition of.