# Finite group with element of prime order

If n is a prime, it has a unique prime decomopsition n = $p_1..p_n$ $a^{n} = a^{{p_i...p_n}^{p_1}} = e$, since each $p_i..p_n \leq n$, $a^{p_i...p_n}$ is indeed an element of prime order $p_1$