show that the integers and , are relatively prime.
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Let and assume .
This implies: and Recall: if then for all
and you should arrive at a contradiction.
Write gcd as a linear combination we have:
(3n+1)x+(5n+2)y=gcd(3n+1,5n+2) if, and only if x,y are naturals and form the smaller combination.
let x=-5 and y=3, then: