Question

What is the remainder when $4^{96}$ is divided by 6? what is cyclicity ?

Answer 1

Finding out the cyclicity,
$\begin{array}{cccccccccc}Number/6& \to & 4^1& 4^2& 4^3& 4^4& 4^5& 4^6& 4^7& 4^8\\ Remainder& \to & 4& 4& 4& 4& 4& 4& 4& 4\end{array}$