1. The problem statement, all variables and given/known data Prove that there exist arbitrarily long arithmetic progressions formed of different positive integers such that every two terms of these progressions are relatively prime. 3. The attempt at a solution I first thought of looking at odd numbers separated by a powers of 2 but I don't think this forms a progression. It seems weird to me because if I have a+bx where a and b are fixed constants so I am adding a multiple of x eventually x will equal a and then 2a so they wont be relatively prime. unless its like how we can have arbitrarily long composite numbers because of n!+2.....n!+n then I could just maybe add a multiple of the prime between n! and 2n!.