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Problem in 1995 Bulgaria MO (Number Theory)

Source:

December 9, 2015
number theory

Problem Statement

Suppose that xx and yy are different real numbers such that xn−ynx−y\frac{x^n-y^n}{x-y} is an integer for some four consecutive positive integers nn. Prove that xn−ynx−y\frac{x^n-y^n}{x-y} is an integer for all positive integers n.
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