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OlympiadBench / 1866 / Define P(n)=n²+n+1. For any positive integers a and b, the set

Problem

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

answer type

Numerical

is multiple answer

false

language

English

question

Define

P(n)=n^{2}+n+1

. For any positive integers

a

and

b

, the set

\{P(a), P(a+1), P(a+2), \ldots, P(a+b)\}

is said to be fragrant if none of its elements is relatively prime to the product of the other elements. Determine the smallest size of a fragrant set.

Plain-text mathematical notation (without MathML)

Define P(n)=n²+n+1. For any positive integers a and b, the set

{P(a),P(a+1),P(a+2),…,P(a+b)}

is said to be fragrant if none of its elements is relatively prime to the product of the other elements. Determine the smallest size of a fragrant set.

Original LaTeX notation

Define $P(n)=n^{2}+n+1$. For any positive integers $a$ and $b$, the set

$$
\{P(a), P(a+1), P(a+2), \ldots, P(a+b)\}
$$

is said to be fragrant if none of its elements is relatively prime to the product of the other elements. Determine the smallest size of a fragrant set.

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1866
task_id: 2609a701-0625-5c4f-8898-d69ce3d0eb38
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1866
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import