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Omni-MATH / Let f : mathbb Q to mathbb Q be a function such that for any x,y in mathbb Q, the number f(x+y)−f(x)−f(y) is an integer. Decide whether it follows that there exists a constant c su…

Problem

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problem

Let $f : \mathbb Q \to \mathbb Q$ be a function such that for any $x,y \in \mathbb Q$, the number f(x+y)−f(x)−f(y)f(x+y)-f(x)-f(y) is an integer. Decide whether it follows that there exists a constant cc such that f(x)−cxf(x) - cx is an integer for every rational number xx.
Plain-text mathematical notation (without MathML)
Let $f : \mathbb Q \to \mathbb Q$ be a function such that for any $x,y \in \mathbb Q$, the number f(x+y)−f(x)−f(y) is an integer. Decide whether it follows that there exists a constant c such that f(x)−cx is an integer for every rational number x.
Original LaTeX notation
Let $f : \mathbb Q \to \mathbb Q$ be a function such that for any $x,y \in \mathbb Q$, the number $f(x+y)-f(x)-f(y)$ is an integer. Decide whether it follows that there exists a constant $c$ such that $f(x) - cx$ is an integer for every rational number $x$.

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Source and history

task_id
1ecd5703-b911-583a-b76c-ca2acc82e483
task_key
test--1ecd5703-b911-583a-b76c-ca2acc82e483
task_revision_id
1
config / split
/ test

Official source

initial import