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OlympiadBench / 2084 / Determine all functions f from the set of positive integers into the set of…

Problem

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

question

Determine all functions

f

from the set of positive integers into the set of positive integers such that for all

x

and

y

there exists a non degenerated triangle with sides of lengths

x, \quad f(y) \text { and } f(y+f(x)-1) .

Plain-text mathematical notation (without MathML)

Determine all functions f from the set of positive integers into the set of positive integers such that for all x and y there exists a non degenerated triangle with sides of lengths

x, f(y) and f(y+f(x)−1).

Original LaTeX notation

Determine all functions $f$ from the set of positive integers into the set of positive integers such that for all $x$ and $y$ there exists a non degenerated triangle with sides of lengths

$$
x, \quad f(y) \text { and } f(y+f(x)-1) .
$$

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: 2084
task_id: a30ccef7-73db-5eb7-b84a-09e76887519c
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--2084
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import