Question

How can I use Euler's generalization of Fermat's little theorem to compute\[18!\text{ }(\text{mod }437)?\]

Answer 1

hmm \(437=23\times 19\) so my guess is to first find the remainders mod 19 and 23

Answer 2

\[18!\equiv -1(19) \] by wilson's which says \((n-1)!\equiv -1(n)\) now what to do with the 23?

Answer 3

guess didn't use euler so maybe this is not the right approach, but i think you can do something similar with the 23 that is compute \(22!\equiv -1(23)\) and then rewrite \(22!=22\times 21\times 20\times 19\times 18!\)

Answer 4

That's an interesting approach. Thanks!