MathDB

5

Part of 2015 Romanian Master of Mathematics

Problems(1)

Integers satisfying an inequality

Source: RMM 2015 Problem 5

3/1/2015
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.
RMMnumber theoryprime numbers