Find the remainder when $2(26!)$ is divided by $29$.
So I know I'm going to use Wilson's theorem and then I would have $28!=-1(\mod29\:)$ but what is the next step? Step by Step explanation please!
[Math] Find the remainder when $2(26!)$ is divided by $29$.
elementary-number-theory
Best Answer
$\begin{eqnarray} {\bf Hint}\ \ \ {\rm mod}\ 29\!:\,\ {-}1\! \overset{\rm Wilson}\equiv 28!\, \equiv &&\ (\color{#c00}{28})\ (\color{#0a0}{27})26!\\ \equiv&& (\color{#c00}{-1})(\color{#0a0}{-2}) 26!\\ \equiv &&\qquad\ \ \,2\cdot 26!\end{eqnarray}$