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Floor of square root

Source: APMO 2013, Problem 2

May 3, 2013
modular arithmeticinequalitiesquadraticsfunctionalgebrafloor functionHi

Problem Statement

Determine all positive integers nn for which n2+1[n]2+2\dfrac{n^2+1}{[\sqrt{n}]^2+2} is an integer. Here [r][r] denotes the greatest integer less than or equal to rr.
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