Erdős–Straus Conjecture: The Sole Tractable Open Problem in Competition Math — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Survey of open competition-style math problems reveals no new solved results; the Erdős–Straus conjecture is the only concrete, tractable open problem with explicit arithmetic structure. | MATH: Erdős–Straus conjecture: for every integer n ≥ 2, there exist positive integers x, y, z such that 4/n = 1/x + 1/y + 1/z. Equivalent to finding integer solutions to 4xyz = n(xy + xz + yz). No counterexample known; verified for n up to ~10^17 (computational bounds vary). | CONNECTION: The equation 4/n = 1/x + 1/y + 1/z is a unit fraction decomposition — related to Egyptian fractions, which historically connect to base-60 (sexagesimal) arithmetic used by Babylonians for such decompositions. The structure of solutions often involves modular constraints (n ≡ 0, 1, 2, 3 mod 4) and prime factor patterns; no direct golden-ratio or crystallographic symmetry appears in the conjecture itself. | DEPTH: 3 — The finding is a catalog of open problems, not a new mathematical result. The Erdős–Straus c Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204104542
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