- #1
Suyogya
- 14
- 0
"If a prime p divides the product ab of two integers a and b,then p must divide at least one of those integers a and b."(its euclid lemma true for primes only) when i tried to prove it as:
let for any integer p divides ab (ab)=(pn) ;for some integer n (a*b)/p=n
since RHS is integer, therefore for LHS to be integer either (a/p) or (b/p) or both must be integer, which means either p divides a or b or both.(hence proved)
But there is no restriction on p to be prime yet? is there any mistake in it?
let for any integer p divides ab (ab)=(pn) ;for some integer n (a*b)/p=n
since RHS is integer, therefore for LHS to be integer either (a/p) or (b/p) or both must be integer, which means either p divides a or b or both.(hence proved)
But there is no restriction on p to be prime yet? is there any mistake in it?