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Math Help - Binomial Theorem:-

  1. #1
    Junior Member
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    Jul 2009
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    40

    Unhappy Binomial Theorem:-

    Find the remainder when 5^99 is divided by 13.
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  2. #2
    Junior Member
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    Aug 2009
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    Gothenburg, Sweden
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    37
    By Fermats little 5^{12} \equiv 1 \pmod {13} so 5^{99}=5^{12 \cdot 8}\cdot 5^{3} \equiv 5^3 \pmod{13}
    It's left to find the rest for 5^3 when it's divided by 13 and I leave this to you.
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