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Romania NMO 2022 Grade 9 P3

Source: Romania National Olympiad 2022

April 21, 2022

functionalgebraromania

Problem Statement

Determine all functions

f:\mathbb{R}\to\mathbb{R}

for which there exists a function

g:\mathbb{R}\to\mathbb{R}

such that

f(x)+f(y)=\lfloor g(x+y)\rfloor

for all real numbers

x

and

y

.
Emil Vasile

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