2016 UMO Problems/Problem 6

Problem

Find all positive integer pairs $(u,m)$ such that $u + m^2$ is divisible by $um-1$ .

$(1,2),(1,3),(2,1),(2,2),(2,5),(3,1),(3,5),(5,2),(5,3)$

2016 UMO (Problems • Answer Key • Resources)
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