36th Austrian Mathematical Olympiad 2005
Source: round 1, problem 4
February 11, 2009
arithmetic sequencegeometric sequencealgebra unsolvedalgebra
Problem Statement
Prove: if an infinte arithmetic sequence ( a_n\equal{}a_0\plus{}nd) of positive real numbers contains two different powers of an integer , then the sequence contains an infinite geometric sequence ( b_n\equal{}b_0q^n) of real numbers.