olymmath

OME 2016 Problem 2

    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 .

    Dataset text AI-MO AoPS. Quoted with source.

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