Problem

Source: Thailand TSTST 2024 P3

Tags: number theory, primitive root



Recall that for an arbitrary prime p, we define a primitive root modulo p as an integer r for which the least positive integer v such that r^{v}\equiv 1\pmod{p} is p-1. Prove or disprove the following statement: For every prime p>2023, there exists positive integers 1\leqslant a<b<c<p such that a,b and c are primitive roots modulo p but abc is not a primitive root modulo p.