Considerable different arithmetic progressions
Source: 40th Austrian Mathematical Olympiad 2009, round 1, problem 4
August 5, 2009
geometric sequencenumber theory proposednumber theory
Problem Statement
Two infinite arithmetic progressions are called considerable different if the do not only differ by the absence of finitely many members at the beginning of one of the sequences.
How many pairwise considerable different non-constant arithmetic progressions of positive integers that contain an infinite non-constant geometric progression with b_2\equal{}40 \cdot 2009 are there?