# Math Help - solve congruences

1. ## solve congruences

3x^5=1 (mod 29)

and

3^x=2 (mod 29)

find all solutions for both congruences.

2. Originally Posted by mathisthebestpuzzle
3x^5=1 (mod 29)
Write, $x^5 \equiv 10(\bmod 29)$ (since $10$ is an inverse of $3$ mod $29$).
Now find the index of $10$ for a given primitive root of $29$.
Can you finish up the problem?

3. hacker i thank you so much, but i had already solved that one since i posted it.

i am stuck on the second one though...any help would be wonderful!