Euler Type Generalization of Wilson's Theorem

Mehdi Hassani, Mahmoud Momeni-Pour

In this short note, we introduce an Euler analogue of Wilson's theorem; $a_1{a}_2...a_{\varphi (n)}\equiv (-1{)}^{\varphi (n)+1}(\mathrm{mod}n)$ say, where $\gcd (a_i,n)=1$.