I was hoping you could help me prove Euclid's lemma using induction. I want to show by induction that if a prime p, divides a product of n numbers, then it divides at least one of the numbers.
I've attempted this myself but what I attempted did not make sense to me. I tried taking the approach that if p|a1a2...an then looking at the case n=1 if p|a1 then we're done by hypothesis and that didn't seem right to me because I kept going in a loop. Help!