Chapter 8.4, Problem 41ES

To determine

(a)

To prove:

For all positive integers $s,\text{ if }p\text{ and }{q}_1,q_2,\mathrm{...},q_s$ are prime numbers and $p|q_1{q}_2\mathrm{....}{q}_s\text{ then }p=q_i$ for some $i$ with $1\le i\le s,$ using mathematical induction and with Euclid’s lemma

To determine

(b)

To prove:

The uniqueness part of the unique factorization theorem for integers.