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$a_n=[n+\sqrt{2}+\frac{1}{2}]$

Source: 2-nd Taiwanese Mathematical Olympiad 1993

January 13, 2007
algebra proposedalgebra

Problem Statement

A sequence (an)(a_{n}) of positive integers is given by an=[n+n+12]a_{n}=[n+\sqrt{n}+\frac{1}{2}]. Find all of positive integers which belong to the sequence.
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