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Simple FE on National Contest

Source: INAMO 2023 P2 (OSN 2023)

August 29, 2023
functional equationalgebrafloor functionFloorIndonesia

Problem Statement

Determine all functions f:R→Rf : \mathbb{R} \to \mathbb{R} such that the following equation holds for every real x,yx,y: f(f(x)+y)=⌊x+f(f(y))⌋. f(f(x) + y) = \lfloor x + f(f(y)) \rfloor. Note: ⌊x⌋\lfloor x \rfloor denotes the greatest integer not greater than xx.
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