# Number theory problem

## 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

## Answers and Replies

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

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