Prove that any integer has either a divisor and or no divisor and (In the latter case it is called a prime).
Prove this statement from the axioms governing the behavior of integers.
Prove that any integer has either a divisor and or no divisor and (In the latter case it is called a prime).
Prove this statement from the axioms governing the behavior of integers.
Suppose has a proper divisor , then there exists an integer such that:
Now if there is nothing left to do, so assume , then:
which implies that which is a factor
Which leaves you tidy this up and sort out the details.
CB
Last edited by CaptainBlack; June 28th 2009 at 02:09 AM.