Artin-Rees theorem

Let $A$ be a Noetherian ring, $𝔞$ an ideal, $M$ a finitely generated module, and $N$ a submodule. Then there exists an integer $k\ge 1$ such that for all integers $n\ge 1$ we have

$${𝔞}^{n}M\cap N={𝔞}^{n-k}({𝔞}^{k}M\cap N).$$