- #1
cragar
- 2,552
- 3
Homework Statement
Prove that there exist arbitrarily long arithmetic progressions formed of different
positive integers such that every two terms of these progressions are relatively prime.
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 won't 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!.