# [Math] Let a and b be relatively prime integers and let k be any integer. Show that a + bk and b are also relatively prime.

combinatorics

Let a and b be relatively prime integers and let k be any integer. Show that a + bk and b are also relatively prime.

IF a+bk and b are relatively prime that means their gcd is 1. But how do I prove that gcd(a+bk,b)=1?

Let integer $d$ divides both $a+bk, b$
$\implies d$ divides $a+bk-k(b)=a$
$\implies d$ divides $a,b$