MathDB

Let

n\geq 3

an integer. Determine whether there exist permutations

(a_1,a_2, \ldots, a_n)

of the numbers

(1,2,\ldots, n)

and

(b_1, b_2, \ldots, b_n)

of the numbers

(n+1,n+2,\ldots, 2n)

so that

(a_1b_1, a_2b_2, \ldots a_nb_n)

is a strictly increasing arithmetic progression.

Problem Statement