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 2 terms of these progressions are relatively prime. 3. The attempt at a solution First i started to think about the odd integers like 2x+1 and how consecutive odd integers are relatively prime because their difference is 2 , but im pretty sure the question is asking about any 2 terms in the progression. Then i started to think about progressions of odd numbers that were separated by powers of 2 but then this would be a progression because the difference between consecutive numbers would not be the same. Then I was trying to think of something i could do with a factorial.