MathDB
SMO Senior Round 2 Qn 5 2013

Source:

June 29, 2013

Problem Statement

Let x,yx,y be distinct real numbers such that xn−ynx−y\frac{x^n-y^n}{x-y} is an integer for 44 consecutive positive integer nn. Prove that xn−ynx−y\frac{x^n-y^n}{x-y} is an integer for all positive integers nn.
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