Use Wilson;s Theorem to find the least nonnegative residue modulo m of integer n n=30! m=31
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Hello, Originally Posted by bigb Use Wilson;s Theorem to find the least nonnegative residue modulo m of integer n n=30! m=31 Wilson's theorem : $\displaystyle (p-1)! \equiv -1 (\bmod p)$ (where p is a prime integer) Here, p=31 and is prime. So $\displaystyle 30! \equiv -1 (\bmod 31)$ But $\displaystyle -1 \equiv 30 (\bmod 31)$ So answer is 30, since you want the least nonnegative residue.
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