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

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- Sep 27th 2010, 03:01 AMFGT12solving cubic congruences
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 - Sep 27th 2010, 05:07 AMundefined
- Sep 27th 2010, 07:18 AMmelese
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 .