# Math Help - residue modulo - wilson's theorem

1. ## 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

2. Originally Posted by htata123
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
$n = \frac{65!}{51!} = \prod_{k=0}^{13}(52 + k) \equiv \prod_{k=0}^{13} (k+1) = 14! =\frac{ 16!}{16\cdot 15} \equiv (-1)(-1)(8) = 8(\bmod 17)$