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Number Theory Level 2

What is the remainder when 22 ! 22! is divided by 23 23 .


The answer is 22.

Danish Ahmed by Danish Ahmed , 24, India

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2 solutions

Danish Ahmed
Aug 17, 2015

If ' p p ' be a prime, then the remainder when ( p − 1 ) ! (p - 1)! is divided by p p is ( p − 1 ) (p-1) .

So here p is 23 23 , so the remainder is 23 − 1 = 22 23 - 1 = 22

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It's called Wilson's theorem .

mathh mathh - 5 years, 10 months ago
Adam Tsou
Aug 17, 2015

(p-2)! 1 (mod p). multiply by (p-1). (p-1)! congruent p-1 congruent -1 (mod p) .

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