The 2011 IMO Windmill Problem and the 1988 IMO Problem 6: A Review of Known Results — E8 Intelligence Research

FINDING: The search results are mostly clickbait YouTube titles and one arXiv proceedings volume; the only substantive mathematical content is the 2011 IMO windmill problem and the 1988 IMO Problem 6 (both well-known). No new unsolved problem or novel equation is presented. | MATH: 2011 IMO Q2 (windmill): Given n≥3 points in general position, a "windmill" process rotates a line about a pivot point, switching pivot to the next point hit; prove that for some pivot and initial line, every point is a pivot infinitely often. Key invariant: the line always separates the point set into two equal-count halves (for odd n, one side has (n−1)/2 points). 1988 IMO Problem 6: Let a,b be positive integers such that ab+1 divides a²+b². Prove (a²+b²)/(ab+1) is a perfect square. The solution uses Vieta jumping: if (a²+b²)/(ab+1)=k, then the quadratic x² − kb·x + (b²−k)=0 has roots a and a' = kb−a; descent on a+b yields k=m². | CONNECTION: The windmill problem's invariant (equal partition) is a discrete Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com