Problem

Source: Romanian IMO Team Selection Test TST 2003, problem 4

Tags: floor function, ratio, geometric sequence, algebra proposed, algebra



Prove that among the elements of the sequence $\left\{ \left\lfloor n\sqrt{2003} \right\rfloor \right\}_{n\geq 1}$ one can find a geometric progression having any number of terms, and having the ratio bigger than $k$, where $k$ can be any positive integer. Radu Gologan