Problem
NT-B2-M04-P020 Wilson as a Criterion
#20
★★★★★ Level 5 of 5
Prove that if \(n>1\) and \((n-1)!\equiv-1\pmod n\), then \(n\) is prime.
Assume \(n\) is composite and take a proper divisor \(d\) of \(n\).
Suppose \(n\) is composite. If \(n=4\), then \(3!=6\equiv2\pmod4\), not \(-1\). Now let \(n\ne4\). Write \(n=ab\), where \(1
This is the strong direction of Wilson; the proof can be expanded in class if needed.