MathNet 2015-part-04 — 191 problems (EN–VI) Question 133

Let $p$ be a prime greater than $3$. For a positive integer $k$, let $R(k)$ denote the remainder of $k$ when divided by $p$. Determine all positive integers $a \lt p$ such that $m + R(ma) \gt a$ for every $m = 1, 2, \dots, p-1$.