(related to Corollary: Prime Dividing Product of Primes Implies Prime Divisor)

- By the generalized Euclidean lemma, there is at least one divisor with $p\mid p_i.$
- Since the prime number $p_i$ has only the trivial divisors $1$ and $p_i$ and since $p\neq 1,$ it follows $p=p_i.$∎

**Landau, Edmund**: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927