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OlympiadBench / 1969 / Determine all functions f:Z→Z satisfying

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

Determine all functions

f: \mathbb{Z} \rightarrow \mathbb{Z}

satisfying

$$
f(f(m)+n)+f(m)=f(n)+f(3 m)+2014
\tag{1}
$$

for all integers

m

and

n

Plain-text mathematical notation (without MathML)

Determine all functions f:Z→Z satisfying

$$
f(f(m)+n)+f(m)=f(n)+f(3 m)+2014
\tag{1}
$$

for all integers m and n.

Original LaTeX notation

Determine all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ satisfying

$$
f(f(m)+n)+f(m)=f(n)+f(3 m)+2014
\tag{1}
$$

for all integers $m$ and $n$.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1969
task_id: 0de3e128-9dfc-56e9-82fe-f8ff503c3c94
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1969
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import