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Problem 1510

National Olympiad, first round

Number theory Difficulty 6.0 Find the answer KöMaL problem A · Hungary · 2023

For real number $r$ let $f(r)$ denote the integer that is the closest to $r$ (if the fractional part of $r$ is 1/2, let $f(r)$ be $r-1/2$ ). Let $a>b>c$ rational numbers such that for all integers $n$ the following is true: $f(na)+f(nb)+f(nc)=n$ . What can be the values of $a$ , $b$ and $c$ ?

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