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Omni-MATH / 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 integer…

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problem

For real number rr let f(r)f(r) denote the integer that is the closest to rr (if the fractional part of rr is 1/21/2, let f(r)f(r) be r−1/2r-1/2). Let a>b>ca>b>c rational numbers such that for all integers nn the following is true: f(na)+f(nb)+f(nc)=nf(na)+f(nb)+f(nc)=n. What can be the values of aa, bb and cc?
Plain-text mathematical notation (without MathML)
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?
Original LaTeX notation
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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task_id
590ce388-5ea5-5c57-8a39-3bbc0bd7c340
task_key
test--590ce388-5ea5-5c57-8a39-3bbc0bd7c340
task_revision_id
1
config / split
/ test

Official source

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