- #1

- 986

- 9

## Homework Statement

Don't have the book with me, but the problem basically asked me to prove that

gcd(

*a*,

*b*)=1 [tex]\Rightarrow[/tex] gcd(

*an*,

*bn*)=

*n*

## Homework Equations

Since

*gcd*(

*a*,

*b*)=1 is a fancy way of saying

*a*and

*b*are relatively prime (or is "

*a*and

*b*are relatively prime" a fancy way of saying gcd(

*a*,

*b*)=1?), I know of a theorem that may prove useful.

__Thm.__If

*a*and

*b*are relatively prime then there exist integers

*m*,

*n*such that

*ma*+

*nb*=1.

## The Attempt at a Solution

It just seems so intuitive ... I don't know where to start.