Wilson?

Number Theory Level 3

True or False?

$n$ divides $(n-1)!$ if and only if $n$ fails to be prime, for any integer $n>1$

True False An open Problem

1 solution

Otto Bretscher
Dec 11, 2018

A counterexample (and, in fact, the only one) is $n=4$ , which fails to divide $3!=6$ . Thus the claim is $\boxed{False}$ .