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Omni-MATH / Let R denote a non-negative rational number. Determine a fixed set of integers a,b,c,d,e,f , such that for every choice of R , |(aR²+bR+c)/(dR²+eR+f)−root[3](2)|<|R−root[3](2)|

Problem

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problem

Let

R

denote a non-negative rational number. Determine a fixed set of integers

a,b,c,d,e,f

, such that for every choice of

R

\left|\frac{aR^2+bR+c}{dR^2+eR+f}-\sqrt[3]{2}\right|<|R-\sqrt[3]{2}|

Plain-text mathematical notation (without MathML)

Let R denote a non-negative rational number. Determine a fixed set of integers a,b,c,d,e,f , such that for every choice of R ,
|(aR²+bR+c)/(dR²+eR+f)−root[3](2)|<|R−root[3](2)|

Original LaTeX notation

Let $R$ denote a non-negative rational number. Determine a fixed set of integers $a,b,c,d,e,f$ , such that for every choice of $R$ ,
$\left|\frac{aR^2+bR+c}{dR^2+eR+f}-\sqrt[3]{2}\right|<|R-\sqrt[3]{2}|$

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task_id: 129db43e-aec1-54bc-ac15-1733f9461a63
task_key: test--129db43e-aec1-54bc-ac15-1733f9461a63
task_revision_id: 3
config / split: / test

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