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equal sets mod p

Source: Mongolian MO 2007 Teachers P3

April 8, 2021
number theory

Problem Statement

Let pp be an odd prime number. Let gg be a primitive root of unity modulo pp. Find all the values of pp such that the sets A={k2+1:1≤k≤p−12}A=\left\{k^2+1:1\le k\le\frac{p-1}2\right\} and B={gm:1≤m≤p−12}B=\left\{g^m:1\le m\le\frac{p-1}2\right\} are equal modulo pp.
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