Friday, August 25, 2017

Proof related with prime numbers and congruence



How to (dis)prove this



(n2)!1modn




If n is said to be a prime number. I guess we'll have to use FERMAT’S LITTLE THEOREM, and I just don't know where to start from. Thanks in advance


Answer



If n=p is a prime, then by Wilson's theorem



1=(p1)!=(p2)!(p1)=(p2)!(modp)1=(p2)!(modp)


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