So far this is what I can do:
Using Fermat's Little Theorem I know that 316≡1(mod17)
Also: 32012=(316)125∗312(mod17)
So I am left with 312(mod17).
Again I'm going to use fermat's theorem so: 312=31634(mod17)
Here I am stuck because I get 3−4(mod17) and I don't know how to calculate this because I don't know what 181(mod17) is.
I know 81=13(mod17)
But I know the answer is 4. What did I do wrong?
Answer
312=(33)4=104 (mod 17), so we have to find 10000 (mod 17), which is evidently 4 (mod 17).
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