Suppose g is a primitive root modulo p (a prime) and suppose m|p-1 (1<m<p-1). How many solutions are there to the congruence:

(mod p)

My attempt:

(mod )

(mod )

(mod )

(mod p)

Hence g=1 which is a contradiction so there are no solutions.

I don't believe my own answer! I have not used the statement that

m|p-1 which tells me that g.c.d(m, = m