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Integers satisfying an inequality

Source: RMM 2015 Problem 5

March 1, 2015
RMMnumber theoryprime numbers

Problem Statement

Let p≥5p \ge 5 be a prime number. For a positive integer kk, let R(k)R(k) be the remainder when kk is divided by pp, with 0≤R(k)≤p−10 \le R(k) \le p-1. Determine all positive integers a<pa < p such that, for every m=1,2,⋯ ,p−1m = 1, 2, \cdots, p-1, m+R(ma)>a. m + R(ma) > a.
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