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OlympiadBench / 1681 / Find all surjective functions f:N→N such that…

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

Find all surjective functions f:N→Nf: \mathbb{N} \rightarrow \mathbb{N} such that for every m,n∈Nm, n \in \mathbb{N} and every prime pp, the number f(m+n)f(m+n) is divisible by pp if and only if f(m)+f(n)f(m)+f(n) is divisible by pp. ( N\mathbb{N} is the set of all positive integers.)
Plain-text mathematical notation (without MathML)
Find all surjective functions f:N→N such that for every m,n∈N and every prime p, the number f(m+n) is divisible by p if and only if f(m)+f(n) is divisible by p.

( N is the set of all positive integers.)
Original LaTeX notation
Find all surjective functions $f: \mathbb{N} \rightarrow \mathbb{N}$ such that for every $m, n \in \mathbb{N}$ and every prime $p$, the number $f(m+n)$ is divisible by $p$ if and only if $f(m)+f(n)$ is divisible by $p$.

( $\mathbb{N}$ is the set of all positive integers.)

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID
1681
task_id
45ee5107-1b9d-58db-95df-070d4f264347
task_key
OE~5fTO~5fmaths~5fen~5fCOMP--train--1681
task_revision_id
1
config / split
OE_TO_maths_en_COMP / train

Official source

initial import