Past exam of the mathematics course of the University of Cambridge / 2017 / ii / Paper 3 / 17G / a / Solution

Burnside's theorem states that every finite group of order $p^a{q}^b$ is solvable, where $p,q$ are primes and $a,b$ are nonnegative integers. In particular, a nonabelian simple group cannot have order divisible by only one or two distinct primes.