Question Number 104659 by bobhans last updated on 23/Jul/20

what is remainder of 12! in mod 17

Answered by bramlex last updated on 23/Jul/20

we can use Wilson′s theorem  by which 16! ≡ −1 (mod 17)  Now use that   16! = 16.15.14.13.12!  16! ≡ (−1)(−2)(−3)(−4).12!  (mod 17 )≡ 12!.7  (mod 17)  because 7.5 ≡ 1 (mod 17)   we get 12! ≡ −5 ≡ 12 (mod 17)