Some proofs use the fact that if a prime number p divides the product of two natural numbers a and b , then p divides either a or b , a statement known as LOCATION@1 's lemma .

To do this , we use the following lemma : if a prime number p divides a product ab , then it divides a or it divides b -LRB- LOCATION@1 's lemma -RRB- .
