Interesting, I didn't even notice that
$$x^6 \equiv 7 \pmod{19}$$
has a similar structure to
$$m\cdot 6 \equiv 6 \pmod{18}$$
It is in fact a non-trivial reduction; we can apply the extended Euclidean algorithm directly to the second congruence but not the first. The fact that the numbers...
Hello,
Please excuse that I won't use LaTeX and can't post links properly; I'm having some issues with the new forum; but I'm happy to see that MHF (Math Help Forum) has both risen from the ashes and gotten a clone. :)
It's not clear to what extent you need to solve this "manually" vs. using...