## $a^m=b^m$ and $a^n=b^n$ imply $a=b$

Let $D$ be an integral domain and let $a^m=b^m$ and $a^n=b^n$ where $m$ and $n$ are relatively prime integers, $a,b \in D$. How do I show $a=b$?

mathematics abstract-algebra ring-theory
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Let $D$ be an integral domain and let $a^m=b^m$ and $a^n=b^n$ where $m$ and $n$ are relatively prime integers, $a,b \in D$. How do I show $a=b$?

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