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Geometric progression in arithmetic sequence

Source: Bosnia and Herzegovina TST 2006 day 2 problem 1

July 14, 2016
algebrageometric sequencearithmetic sequence

Problem Statement

Prove that every infinite arithmetic progression aa, a+da+d, a+2da+2d,... where aa and dd are positive integers, contains infinte geometric progression bb, bqbq, bq2bq^2,... where bb and qq are also positive integers
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