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OlympiadBench / 2075 / Let Z_(>0) be the set of positive integers. Find all functions …

Problem

Answer published by the source. Consult the official source to check your work against its answer.

answer type

Expression

is multiple answer

false

language

English

question

Let

\mathbb{Z}_{>0}

be the set of positive integers. Find all functions

f: \mathbb{Z}_{>0} \rightarrow \mathbb{Z}_{>0}

such that

m^{2}+f(n) \mid m f(m)+n

for all positive integers

m

and

n

Plain-text mathematical notation (without MathML)

Let Z_(>0) be the set of positive integers. Find all functions f:Z_(>0)→Z_(>0) such that

m²+f(n)∣mf(m)+n

for all positive integers m and n.

Original LaTeX notation

Let $\mathbb{Z}_{>0}$ be the set of positive integers. Find all functions $f: \mathbb{Z}_{>0} \rightarrow \mathbb{Z}_{>0}$ such that

$$
m^{2}+f(n) \mid m f(m)+n
$$

for all positive integers $m$ and $n$.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 2075
task_id: 20eeb793-7e0e-572c-b444-2d2f683b153f
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2075
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import