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2007 Spain Mathematical Olympiad, Problem 2

Source: Spain Mathematical Olympiad 2007

June 8, 2017
algebranumber theory

Problem Statement

Determine all the possible non-negative integer values that are able to satisfy the expression: (m2+mn+n2)(mn−1)\frac{(m^2+mn+n^2)}{(mn-1)} if mm and nn are non-negative integers such that mn≠1mn \neq 1.
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