Find all the solutions of
I can only see
and
however i cannot seem to condense these further and mod 11 by inspection does seem right
This is my attempt.
For the first congruence: by Fermat's Theorem, and replacing coefficients modulo 3 gives or .
Similarly, we replace coefficients modulo 11 and hence . Dividing by 3 gives . Here by simply checking integers gives .
Now we have to consider three systems: and ; and ; and . By inspection, the solutions are .