MathDB
Sum of reciprocals of product of pairs is 1

Source: India TST 2023 Practice Test 1 P3

July 9, 2023
algebra

Problem Statement

Prove that for all integers k>2k>2, there exists kk distinct positive integers a1,…,aka_1, \dots, a_k such that ∑1≤i<j≤k1aiaj=1.\sum_{1 \le i<j \le k} \frac{1}{a_ia_j} =1.
Proposed by Anant Mudgal
Back to ProblemsView on AoPS