EGMO 2022 Problem 4 Day 2 Given a positive integer n≥2n \geq 2n≥2, determine the largest positive integer NNN for which there exist N+1N+1N+1 real numbers a0,a1,…,aNa_{0}, a_{1}, \ldots, a_{N}a0,a1,…,aN such that (1) a0+a1=−1na_{0}+a_{1}=-\frac{1}{n}a0+a1=−n1, and (2) (ak+ak−1)(ak+ak+1)=ak−1−ak+1\left(a_{k}+a_{k-1}\right)\left(a_{k}+a_{k+1}\right)=a_{k-1}-a_{k+1}(ak+ak−1)(ak+ak+1)=ak−1−ak+1 for 1≤k≤N−11 \leq k \leq N-11≤k≤N−1. Proposed by: Romania Dataset text NuminaMath olympiads. Quoted with source. Solutions No solution is on olymmath yet. Official and human solutions come first when they arrive. AI solutions come after them, with a label. Add a solution PreviousProblem 3 NextProblem 5 Locator egmo/2022/p4 · Tag 3VZF1QEA58 · Edit this page on GitHub · Keys: j next, k previous