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OlympiadBench / 1736 / Find the least positive integer n for which there exists a 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

Find the least positive integer

n

for which there exists a set

\left\{s_{1}, s_{2}, \ldots, s_{n}\right\}

consisting of

n

distinct positive integers such that

\left(1-\frac{1}{s_{1}}\right)\left(1-\frac{1}{s_{2}}\right) \ldots\left(1-\frac{1}{s_{n}}\right)=\frac{51}{2010}

Plain-text mathematical notation (without MathML)

Find the least positive integer n for which there exists a set {s₁,s₂,…,s_(n)} consisting of n distinct positive integers such that

(1−(1)/(s₁))(1−(1)/(s₂))…(1−(1)/(s_(n)))=(51)/(2010)

Original LaTeX notation

Find the least positive integer $n$ for which there exists a set $\left\{s_{1}, s_{2}, \ldots, s_{n}\right\}$ consisting of $n$ distinct positive integers such that

$$
\left(1-\frac{1}{s_{1}}\right)\left(1-\frac{1}{s_{2}}\right) \ldots\left(1-\frac{1}{s_{n}}\right)=\frac{51}{2010}
$$

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1736
task_id: 648ac744-9d36-5671-b3f0-fe221d46b6e6
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1736
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import