# How to prove the following equality about Integral closure of an ideal in regular local ring of dimension 3?

Let $(R,m)$ be a regular local ring of dimension three and $I$ be an ideal of $R$. Is $\bar{I^{n+1}}=I^n\bar{I}$ for all positive integer $n$? where $\bar{I}$ is integral closure of $I$.

• It is known that the following question is true for regular local ring of dimension 2. – Amir Mafi Sep 7 '16 at 10:18