1

Part of 1993 Taiwan National Olympiad

Problems(1)

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

Source: 2-nd Taiwanese Mathematical Olympiad 1993

(a_{n})

of positive integers is given by

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

. Find all of positive integers which belong to the sequence.

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