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China Mathematical Olympiad 1991 problem4

Source: China Mathematical Olympiad 1991 problem4

October 8, 2013

number theory unsolvednumber theory

Problem Statement

Find all positive integer solutions

(x,y,z,n)

of equation

x^{2n+1}-y^{2n+1}=xyz+2^{2n+1}

, where

n\ge 2

and

z \le 5\times 2^{2n}

.

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