Following the Powers of 2

Number Theory Level pending

x , x, y , y, and z z are non-negative integers. Find the number of ordered triplets ( x , y , z ) (x,y,z) such that x 4 + 8 y 4 + 16 z 4 = 64 x y 3 z 4 x^4+8y^4+16z^4=64xy^3z^4

This problem is an entry in Finn Hulse's Themed Problem Challenge: Week 4 .


The answer is 1.

Trevor B. by Trevor B. , 22, USA

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1 solution

Bogdan Simeonov
May 21, 2014

First notice ( 0 , 0 , 0 ) (0,0,0) is a solution.Then we can look at the case when none of them are 0.I am not going to go through this thoroughly, you just need to use divisibility by 2 and FMID.

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