# Following the Powers of 2

Number Theory Level pending

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

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

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