MathDB

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.

Problem Statement