What is the correct answer to this expression:
2632(mod12)
When I tried in Wolfram Alpha the answer is 4, this is also my answer using Fermat's little theorem, but in a calculator the answer is different, 0.
Answer
First, note that 26≡2(mod12), so 2632≡232(mod12).
Next, note that 24≡16≡4(mod12), so 232≡(24)8≡48(mod12), and 42≡4(mod12).
Finally, 48≡(42)4≡44≡(42)2≡42≡4(mod12).
Then we get the result.
There are slicker solutions with just a few results from elementary number theory, but this is a very basic method which should be easy enough to follow.
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