SOLUTION: Let a and b be relatively prime intergers and let k be any integer. Show that b and a+bk are relatively prime

Algebra ->  Test -> SOLUTION: Let a and b be relatively prime intergers and let k be any integer. Show that b and a+bk are relatively prime      Log On


   

Question 490977: Let a and b be relatively prime intergers and let k be any integer. Show that b and a+bk are relatively prime
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
One way to show this is to show that the fraction (a+bk)/b is irreducible. This fraction splits to (a/b)+k, which is obviously irreducible because a/b is irreducible. Hence, b and a+bk are relatively prime.