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Spain National Mathematical Olympiad 2016 Day 1 Problem 2

Source: OME 2016 Day 1 Problem 2

April 2, 2016
number theoryQuadratic Residuesnational olympiadOlympiadprime numbers

Problem Statement

Given a positive prime number pp. Prove that there exist a positive integer α\alpha such that p∣α(α−1)+3p|\alpha(\alpha-1)+3, if and only if there exist a positive integer β\beta such that p∣β(β−1)+25p|\beta(\beta-1)+25.
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