MathDB

Consider an increasing sequence of real numbers

a_1<a_2<\ldots<a_{2023}

such that all pairwise sums of the elements in the sequence are different. For such a sequence, denote by

M

the number of pairs

(a_i,a_j)

such that

a_i<a_j

and

a_i+a_j<a_2+a_{2022}

. Find the minimal and the maximal possible value of

M

Problem Statement