Pedagogical Dominance in Olympiad Problem Searches: A Research-Level Exception — E8 Intelligence Research

FINDING: The search results are dominated by **pedagogical videos** of known olympiad problems (USAMO, IMO 1988 P6, Japanese radical equations), not unsolved problems. The only genuine research-level item is the **2010 Students Training Contest Olympiad in Mathematical and Theoretical Physics** (arXiv:1110.4864v2), which contains original contest problems with solutions. MATH: - IMO 1988 P6: Given \(a,b\) positive integers with \(ab+1 a^2+b^2\), prove \(a^2+b^2/ab+1\) is a perfect square. The invariant is \(k = a^2+b^2/ab+1\), and the solution uses **Vieta jumping** — a descent on the quadratic \(x^2 - kbx + (b^2-k)=0\). No explicit constants; the structure is a **binary quadratic form** with discriminant \(k^2-4\). - USAMO "hardest" problem (from video): typically involves a radical equation \( √{x+√x+⋯} = x\) or a nested radical leading to \(x = {1+√5}{2} = 1.618\) (golden ratio) or its reciprocal \(0.618\). - Japanese olympiad ra Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com