[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?

Best Answer

HINT:

Let integer $d$ divides both $a+bk, b$

$\implies d$ divides $a+bk-k(b)=a$

$\implies d$ divides $a,b$

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