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 $\displaystyle as+tb=1$ assume that $\displaystyle \gcd(a,b)=d>1$. Then the left hand is divisible by $\displaystyle d$ but the right hand is not a contradiction. Thus,Originally Posted by suedenation
$\displaystyle \gcd(a,b)=1$.
The converse is tricker to prove, maybe I will post the proof later on I cannot post it now.