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OlympiadBench / 1869 / Denote by N the set of all positive integers. Find all functions …

Problem

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

question

Denote by N\mathbb{N} the set of all positive integers. Find all functions f:N→Nf: \mathbb{N} \rightarrow \mathbb{N} such that for all positive integers mm and nn, the integer f(m)+f(n)−mnf(m)+f(n)-m n is nonzero and divides mf(m)+nf(n)m f(m)+n f(n).
Plain-text mathematical notation (without MathML)
Denote by N the set of all positive integers. Find all functions f:N→N such that for all positive integers m and n, the integer f(m)+f(n)−mn is nonzero and divides mf(m)+nf(n).
Original LaTeX notation
Denote by $\mathbb{N}$ the set of all positive integers. Find all functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that for all positive integers $m$ and $n$, the integer $f(m)+f(n)-m n$ is nonzero and divides $m f(m)+n f(n)$.

answer type

Expression

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID
1869
task_id
3221b6a2-b5ae-5b43-a6ba-73d00ae80a1e
task_key
OE~5fTO~5fmaths~5fen~5fCOMP--train--1869
task_revision_id
4
config / split
OE_TO_maths_en_COMP / train

Official source

initial import