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Values that take the maximum integer of m^2+\sqrt{2}n

Source: 2021 Peru Cono Sur P1

July 11, 2023
number theoryfloor function

Problem Statement

Find the set of all possible values of the expression ⌊m2+2n⌋\lfloor m^2+\sqrt{2} n \rfloor, where mm and nn are positive integers. Note: The symbol ⌊x⌋\lfloor x\rfloor denotes the largest integer less than or equal to xx.
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