# residue modulo - wilson's theorem

• Feb 19th 2009, 10:18 AM
htata123
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
• Feb 19th 2009, 10:36 AM
ThePerfectHacker
Quote:

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

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