Use Euclid's Lemma and induction to prove that if p and
q1,q2,q3,...,qn (1,2,3 and n are subscripts) are prime numbers
and p divides q1q2q3...qn ( the product), then p=qi for some
i=1,2,3....n.
Euclid's lemma tells you that this is true for .
Now suppose it true for some , then we have for any prime numbers:
Then by Euclids lemma if then either or . But we already have by assumption that if then divides one of Hence the result if true for is true for , and with the base case we have a proof by induction for all integers
RonL