Abstract Algebra: Theory and Applications · Problem 2.4.18

Groups — Thomas Judson

Mathematics — Abstract Algebra · gcd-linear-combination

Problem

Let

a

and

b

be integers such that

\gcd(a,b) = 1

. Let

r

and

s

be integers such that

ar + bs = 1

. Prove that

\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1.