Euler's Theorem to solve for X $x^{138} \bmod 77 = 25$. How can I use Euler's Theorem to solve for $x$. $77$ is not a prime number but its factors are. $7$ and $11$ are prime, so the totient function of $77$ will be $60$

Using Euler's theorem we get $x^{138}\equiv x^{18} \bmod77$
So we need to find numbers such that $x^{18}\equiv25\bmod77$ So you need to try with all 60 numbers relatively prime to 77.
