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OlympiadBench / 1798 / Determine all integers n≥1 for which there exists a pair of positive…

Problem

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

question

Determine all integers

n \geqslant 1

for which there exists a pair of positive integers

(a, b)

such that no cube of a prime divides

a^{2}+b+3

and

\frac{a b+3 b+8}{a^{2}+b+3}=n

Plain-text mathematical notation (without MathML)

Determine all integers n≥1 for which there exists a pair of positive integers (a,b) such that no cube of a prime divides a²+b+3 and

(ab+3b+8)/(a²+b+3)=n

Original LaTeX notation

Determine all integers $n \geqslant 1$ for which there exists a pair of positive integers $(a, b)$ such that no cube of a prime divides $a^{2}+b+3$ and

$$
\frac{a b+3 b+8}{a^{2}+b+3}=n
$$

answer type

Numerical

is multiple answer

false

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1798
task_id: fd0a4089-bf69-5718-88bf-0d5a3dd5cb26
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1798
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import