This page will contain proofs relating to prime numbers. Because the definitions are quite similar, proofs relating to irreducible numbers will also go on this page.
Definition of PrimeEdit
A prime number p>1 is one whose only positive divisors are 1 and p.
Theorem: is prime and implies that or .
Proof: Let's assume that is prime and , and that . We must show that .
Let's consider . Because is prime, this can equal or . Since we know that .
By the gcd-identity, for some .
When this is multiplied by we arrive at .
Because and we know that , and that , as desired.