MathDB
Lots of odd and even numbers

Source: RMO 2006, 10th grade

April 17, 2006
floor functionalgebra proposedalgebra

Problem Statement

Prove that among the elements of the sequence (⌊n2⌋+⌊n3⌋)n≥0\left( \left\lfloor n \sqrt 2 \right\rfloor + \left\lfloor n \sqrt 3 \right\rfloor \right)_{n \geq 0} are an infinity of even numbers and an infinity of odd numbers.
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