## [Hints] 2015 Kazakhstan NMO Problem 2

2015 Kazakh NMO 2. Solve in positive integers

$x^y y ^x = (x+y)^z$

Hint 1: Can you find solutions for $x = 1$ or $y = 1$? How about for $x = y$?

Scroll down for Hint 2…

Hint 2: Pick a prime $p$ which is a divisor of $x$, and let $p^\alpha \| x$, i.e. $p^\alpha \mid x$ but $p^{\alpha + 1} \nmid x$. Prove that we must have $p^\alpha \| y$.