Chapter 4.3, Problem 37E

(a)

To determine

To prove: That $\sim$ defines an equivalence relation on N for positive integers $a$ and $b$, where $a\sim b$ is true if there exist integers $n\ge 1$ and $m\ge 1$ such that $a^m=b^n$.

(b)

To determine

The value of $\overline{3},\overline{4}$, and $\overline{144}$.

(c)

To determine

The equivalence class of $a\in N$.