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OlympiadBench / 1938 / Determine all functions f:Z→Z with the property…

Problem

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

question

Determine all functions

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

with the property that

$$
f(x-f(y))=f(f(x))-f(y)-1
\tag{1}
$$

holds for all

x, y \in \mathbb{Z}

Plain-text mathematical notation (without MathML)

Determine all functions f:Z→Z with the property that

$$
f(x-f(y))=f(f(x))-f(y)-1
\tag{1}
$$

holds for all x,y∈Z.

Original LaTeX notation

Determine all functions $f: \mathbb{Z} \rightarrow \mathbb{Z}$ with the property that

$$
f(x-f(y))=f(f(x))-f(y)-1
\tag{1}
$$

holds for all $x, y \in \mathbb{Z}$.

answer type

Expression

is multiple answer

true

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1938
task_id: bbc0b132-c034-522d-842d-a36c420dd288
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1938
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import