MathDB

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}

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

Problem Statement