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.	Choose the correct answer
A) (a+n, b+n) = 50  B) 4  C) 3  D) 2  E) (a+n, b+n) = 1
Let a ,and b be two different integers. Assume for instance a &lt; b, and let n = (b-a)k+ I-a. For k sufficiently large, n will be positive integer. We have a+n = (b-a)k+l, b+n = (b-a) (k+l)+l, hence a+n and b+n will be positive integers. If we had d|a+n and d|b+n, we would have d|a-b, and, in view of d|a+n, also d|1, which implies that d = 1. Thus, (a+n, b+n) = 1.   So Answer is (a+n, b+n) = 1 (a+n, b+n) = 1
<result>E</result>
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.