Modular Arithmetic/Wilson's Theorem

Examples

5 is a prime number because,

$4!=24$

and

$24\equiv -1(\mathrm{mod}5)⟹25|5$

which is true. 6, on the other hand, is not, as

$5!=120$

and

$120\equiv -1(\mathrm{mod}6)⟹121|6$

which is false. Template:Bookcat