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Geometric progression among the numbers n\sqrt 2003

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

September 24, 2005
floor functionratiogeometric sequencealgebra proposedalgebra

Problem Statement

Prove that among the elements of the sequence {⌊n2003⌋}n≥1\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 kk, where kk can be any positive integer. Radu Gologan
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