## Unique factorization

After receiving many questions from students, I recalled that I was myself quite unhappy with the proof that I presented of the unique factorization theorem as well as the theorem on infinitude of primes. As a general principle, it’s good to avoid proofs by contradiction. In fact, in my own research papers, I don’t think I’ve ever given a proof by contradiction.

In Monday’s lecture, I’ll present a more straightforward proof by induction of both theorems.

1. Kunal Patel
$p_1p_2\cdots p_n+1.$