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Regional Olympiad - FBH 2009 Grade 10 Problem 4

Source: Regional Olympiad - Federation of Bosnia and Herzegovina 2009

September 28, 2018
number theoryInteger

Problem Statement

Let xx and yy be positive integers such that x2−1y+1+y2−1x+1\frac{x^2-1}{y+1}+\frac{y^2-1}{x+1} is integer. Prove that numbers x2−1y+1\frac{x^2-1}{y+1} and y2−1x+1\frac{y^2-1}{x+1} are integers
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