# Meaning of double vertical bars in context: “let $q$ be a prime divisor of $n$ with $q^s|| n$.”

I've been doing some reading about the AKS primality test. I specifically have been reading this. On page 19, I don't understand the notation involving the double vertical bars: Let $q$ be a prime divisor of $n$ with $q^s|| n$.

Does anyone know what this means?

• I've seen it used sometimes with the meaning that $q^s\mid n$ but $q^{s+1}\nmid n$. – JiK Mar 30 '14 at 11:50

It means that $s$ is the greatest natural number such that $q^s$ divides $n$. Therefore $q^s$ divides $n$ but $q^{s+1}$ doesn't divide $n$.