Number Theory Problem: Proving (a,b)=1 if a|c and b|c

[yeland404]

Homework Statement

a,b,c belong to Z with (a,b)=1. Prove that if a|c and b|c, then ab|c

Homework Equations

let a1,a2...an, c belong to Zwith a1...an pairwise relatively prime, prove if ai|c for each i, then a1a2...an|c

The Attempt at a Solution

if a|c, then c=ea, b|c, then c=fb, then which the next step and how it relates with (a,b)=1

 

[Poopsilon]

(a,b)=1, thus consider the prime factorization of e.

 

[damianou]

There exists integers x, y such that ax+by=1. Therefore c=acx+bcy=abrx+basy.