MathDB

A fractional number

x

is called pretty if it has finite expression in base

-b

numeral system,

b

is a positive integer in

[2;2022]

. Prove that there exists finite positive integers

n\geq 4

that with every

m

(\frac{2n}{3}; n)

then there is at least one pretty number between

\frac{m}{n-m}

and

\frac{n-m}{m}

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