(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

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.

2. Relevant 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.

3. 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

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# Prime Divisor Problem

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