MathDB

Let

M

be a set of

13

positive integers with the property that

\forall \ m\in M, \ 100\leq m\leq 999

. Prove that there exists a subset

S\subset M

and a combination of arithmetic operations (addition, subtraction, multiplication, division – without using parentheses) between the elements of

S

, such that the value of the resulting expression is a rational number in the interval

(3,4)

Problem Statement