MathDB

5

Part of 2013 Singapore Senior Math Olympiad

Problems(1)

SMO Senior Round 2 Qn 5 2013

Source:

6/29/2013
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.