Question 47
Determine all natural numbers $n \ge 2$ with the property that there are two permutations $(a_1, a_2, \dots, a_n)$ and $(b_1, b_2, \dots, b_n)$ of the numbers $1, 2, \dots, n$ such that $(a_1 + b_1, a_2 + b_2, \dots, a_n + b_n)$ are consecutive natural numbers.