- #1

- 40

- 0

## Homework Statement

I have to prove the following:

Let a

_{1},a

_{2}, ...,a

_{n}be integers and set b=a

_{1}*a

_{2}*...*a

_{n}. If c is a nonzero integer and c is relatively prime to each a

_{k}, then c and b are relatively prime.

## Homework Equations

Definition of relatively prime: Let a and b be integers, not both zero. if gcd(a,b)=1 then a and b are relatively prime.

## The Attempt at a Solution

1. Let a

_{1},a

_{2}, ...,a

_{n}be integers and let b=a

_{1}*a

_{2}*...*a

_{n}. Suppose there exists a nonzero integer c where c is relatively prime to each a

_{k}.

2. By defn, gcd(c,a

_{k})=1

I need help showing that the gcd(c,a

_{1}*a

_{2})=1

Thanks

Last edited: