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Vietnamese Olympiad national 2007, problem 2

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February 8, 2007
number theory unsolvednumber theory

Problem Statement

Let x,yx,y be integer number with x,y≠−1x,y\neq-1 so that x4−1y+1+y4−1x+1∈Z\frac{x^{4}-1}{y+1}+\frac{y^{4}-1}{x+1}\in\mathbb{Z}. Prove that x4y44−1x^{4}y^{44}-1 is divisble by x+1x+1
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