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Omni-MATH / Find the smallest constant C>0 for which the following statement holds: among any five positive real numbers a₁,a₂,a₃,a₄,a₅ (not necessarily distinct), one can always choose distin…

Problem

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problem

Find the smallest constant C>0C > 0 for which the following statement holds: among any five positive real numbers a1,a2,a3,a4,a5a_1,a_2,a_3,a_4,a_5 (not necessarily distinct), one can always choose distinct subscripts i,j,k,li,j,k,l such that |aiaj−akal|≤C. \left| \frac{a_i}{a_j} - \frac {a_k}{a_l} \right| \le C.
Plain-text mathematical notation (without MathML)
Find the smallest constant C>0 for which the following statement holds: among any five positive real numbers a₁,a₂,a₃,a₄,a₅ (not necessarily distinct), one can always choose distinct subscripts i,j,k,l such that
|(a_(i))/(a_(j))−(a_(k))/(a_(l))|≤C.
Original LaTeX notation
Find the smallest constant $C > 0$ for which the following statement holds: among any five positive real numbers $a_1,a_2,a_3,a_4,a_5$ (not necessarily distinct), one can always choose distinct subscripts $i,j,k,l$ such that
\[ \left| \frac{a_i}{a_j} - \frac {a_k}{a_l} \right| \le C. \]

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Source and history

task_id
e4d98b06-c4b9-5c21-9c1b-d41f2eadecc1
task_key
test--e4d98b06-c4b9-5c21-9c1b-d41f2eadecc1
task_revision_id
1
config / split
/ test

Official source

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