# Math Help - Relatively Prime

1. ## Relatively Prime

Does anyone how to prove the following:

a and b are relatively prime if and only if There exist integers s and t satisfying sa + tb = 1

Thanks very much!!!

2. Originally Posted by suedenation
Does anyone how to prove the following:

a and b are relatively prime if and only if There exist integers s and t satisfying sa + tb = 1

Thanks very much!!!
If $as+tb=1$ assume that $\gcd(a,b)=d>1$. Then the left hand is divisible by $d$ but the right hand is not a contradiction. Thus,
$\gcd(a,b)=1$.

The converse is tricker to prove, maybe I will post the proof later on I cannot post it now.