[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.

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