MathDB
sorting sums (a_i +a_j) in ascending order, arithmetic progression when?

Source: Dutch IMO TST 2016 day 3 p2

August 30, 2019
arithmetic sequencealgebrasums

Problem Statement

For distinct real numbers a1,a2,...,ana_1,a_2,...,a_n, we calculate the n(n−1)2\frac{n(n-1)}{2} sums ai+aja_i +a_j with 1≤i<j≤n1 \le i < j \le n, and sort them in ascending order. Find all integers n≥3n \ge 3 for which there exist a1,a2,...,ana_1,a_2,...,a_n, for which this sequence of n(n−1)2\frac{n(n-1)}{2} sums form an arithmetic progression (i.e. the di erence between consecutive terms is constant).
Back to ProblemsView on AoPS