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OlympiadBench / 1838 / Find the smallest real constant C such that for any positive real numbers…

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 smallest real constant

C

such that for any positive real numbers

a_{1}, a_{2}, a_{3}, a_{4}

and

a_{5}

(not necessarily distinct), one can always choose distinct subscripts

i, j, k

and

l

such that

$$
\left|\frac{a_{i}}{a_{j}}-\frac{a_{k}}{a_{l}}\right| \leqslant C .\tag{1}
$$

Plain-text mathematical notation (without MathML)

Find the smallest real constant C such that for any positive real numbers a₁,a₂,a₃,a₄ and a₅ (not necessarily distinct), one can always choose distinct subscripts i,j,k and l such that

$$
\left|\frac{a_{i}}{a_{j}}-\frac{a_{k}}{a_{l}}\right| \leqslant C .\tag{1}
$$

Original LaTeX notation

Find the smallest real constant $C$ such that for any positive real numbers $a_{1}, a_{2}, a_{3}, a_{4}$ and $a_{5}$ (not necessarily distinct), one can always choose distinct subscripts $i, j, k$ and $l$ such that

$$
\left|\frac{a_{i}}{a_{j}}-\frac{a_{k}}{a_{l}}\right| \leqslant C .\tag{1}
$$

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1838
task_id: 6f402411-6736-5d8a-bf86-6b1aeb410670
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1838
task_revision_id: 1
config / split: OE_TO_maths_en_COMP / train

Official source

initial import