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Math Help - residue modulo - wilson's theorem

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    residue modulo - wilson's theorem

    Need help with this;

    Use wilson's theorem to find the lest nonnegative residue modulo m of each integer n below

    n = (65!)/(51!), m = 17
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  2. #2
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    Quote Originally Posted by htata123 View Post
    Need help with this;

    Use wilson's theorem to find the lest nonnegative residue modulo m of each integer n below

    n = (65!)/(51!), m = 17
    n = \frac{65!}{51!} = \prod_{k=0}^{13}(52 + k) \equiv \prod_{k=0}^{13} (k+1) = 14! =\frac{ 16!}{16\cdot 15} \equiv (-1)(-1)(8) = 8(\bmod 17)
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