P1

Part of 2021 Peru Cono Sur TST.

Problems(1)

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

Source: 2021 Peru Cono Sur P1

Find the set of all possible values of the expression

\lfloor m^2+\sqrt{2} n \rfloor

m

n

are positive integers. Note: The symbol

\lfloor x\rfloor

denotes the largest integer less than or equal to

x

number theoryfloor function