I have a question about the gcd(a,m) in this type problem.
for example....

7x^20 = = 34(mod 37) [using indices]
I (7x^20) = I(34) (mod 36)
...
...
..
.
20x = 27(mod 36) here I would take the gcd (20,36) = 4 divided by 27/\ therefore there are no solutions???

Is this accurate?