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Obtain residue class of $7^{9999}$ modulo 100 using the Little Fermat theorem.

But I have no idea how to proceed.

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    I would rather use Euler's theorem: http://en.wikipedia.org/wiki/Euler's_theorem2012-03-26
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    It can be done using just basic tools. But I believe that if we are going to use something related to Fermat's Theorem, we really want to use Euler's generaliation of Fermat's Theorem.2012-03-26
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    An hint on how to proceed with basic tools is to compute $7^4$ mod $100$ and then observe that...2012-03-26
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    Have you looked at the first link on the right-hand side? http://math.stackexchange.com/questions/12846/using-fermats-little-theorem2012-03-26

4 Answers 4