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Numbers of the form n = k + 2[sqrt(k)] + 2 where k in N

Source: XIV Rioplatense Mathematical Olympiad (2005), Level 3

July 26, 2011

floor functionnumber theory unsolvednumber theory

Problem Statement

Find all numbers

n

that can be expressed in the form

n=k+2\lfloor\sqrt{k}\rfloor+2

for some nonnegative integer

k