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Solve for x, y, z, t

Source: 2019 Jozsef Wildt International Math Competition

May 20, 2020
number theory

Problem Statement

Prove that exist different natural numbers xx, yy, zz, tt for which 256×2019180n+1=2x9−2y6+z5−t4256\times 2019^{180n+1}=2x^9-2y^6+z^5-t^4for all n∈N∗n\in \mathbb{N}^*
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