44. Prove that if a and b are different integers, then there exist infinitely
many positive integers n such that a+n and b+n are relatively prime.
Let and be two different integers. Assume for instance , and let . For sufficiently large will be positive integer. We have , , hence and will be positive integers. If we had and , we would have , and, in view , also , which implies that , Thus .
Comments
Leave a comment