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    OlympiadHardNumber Theory10–12

    Fermat's Little Theorem

    Pequeno Teorema de Fermat

    Find the remainder when 2^{100} is divided by 101.

    101 is prime. Use Fermat's Little Theorem: a^{p-1} \equiv 1 \pmod{p}.

    Solution

    Step 1 of 3

    1. 1.101 is prime and \gcd(2, 101) = 1.