MathDB

Let

n

be a positive integer. For each partition of the set

\{1,2,\dots,3n\}

into arithmetic progressions, we consider the sum

S

of the respective common differences of these arithmetic progressions. What is the maximal value that

S

can attain?
(An arithmetic progression is a set of the form

\{a,a+d,\dots,a+kd\}

, where

a,d,k

are positive integers, and

k\geqslant 2

; thus an arithmetic progression has at least three elements, and successive elements have difference

d

, called the common difference of the arithmetic progression.)

Problem Statement