MathDB

The

2m

numbers 1\cdot 2, 2\cdot 3, 3\cdot 4,\hdots,2m(2m+1) are written on a blackboard, where

m\geq 2

is an integer. A move consists of choosing three numbers

a, b, c

, erasing them from the board and writing the single number

\frac{abc}{ab+bc+ca}

After

m-1

such moves, only two numbers will remain on the blackboard. Supposing one of these is

\tfrac{4}{3}

, show that the other is larger than

4

Problem Statement