Problem

Source: India TST 2023 Practice Test 1 P3

Tags: algebra



Prove that for all integers $k>2$, there exists $k$ distinct positive integers $a_1, \dots, a_k$ such that $$\sum_{1 \le i<j \le k} \frac{1}{a_ia_j} =1.$$ Proposed by Anant Mudgal