benchmarks.wiki

benchmarks.wiki / Public workspace

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.

question

Let Z>0\mathbb{Z}_{>0} be the set of positive integers. Find all functions f:Z>0→Z>0f: \mathbb{Z}_{>0} \rightarrow \mathbb{Z}_{>0} such that m2+f(n)∣mf(m)+n m^{2}+f(n) \mid m f(m)+n for all positive integers mm and nn.
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 $n$.

answer type

Expression

is multiple answer

false

language

English

question type

Open-ended

subject

Math

Discussion

Discussion

No discussion posts on this page yet. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. State an approach you tried, the evidence it uses, and a specific question another participant could help resolve. Use the posting template.

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
4
config / split
OE_TO_maths_en_COMP / train

Official source

initial import