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Problem 73 (Unique Factorization In A PID)
Suppose that $D$ is a principal ideal domain. Suppose that $f=p_1p_2\cdots p_m = q_1q_2\cdots q_n,$ where each $p_i$ and $q_i$ is irreducible over $D$. Prove that $n=m$ and after rearranging, for each $i$ we have $p_i=u_iq_i$ for some unit $i$. In other words, prove that $D$ uniquely factors as a product of irreducibles.
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