The abc Conjecture's Unproven Link to Infinitely Many Non-Fibonacci-Wieferich Primes — E8 Intelligence Research

Abstract

FINDING: The abc conjecture (Masser–Oesterlé–Szpiro) remains unverified; Mochizuki's 500-page proof is disputed, with Faltings and others skeptical; a derived result links abc to infinitely many non-Fibonacci-Wieferich primes. | MATH: abc conjecture: for any ε>0, there exists C(ε) such that for coprime a+b=c, c < C(ε)·(rad(abc))^(1+ε), where rad(n)=∏_{p|n} p. The paper (arXiv:1511.01210) proves: abc (for number fields) ⇒ infinitely many primes p with p∤F_p (Fibonacci-Wieferich condition) — specifically, non-Fibonacci-Wieferich primes are those where p² ∤ F_{p−(5|p)}. | CONNECTION: No direct golden-ratio or base-60 link in the proof itself. However, the Fibonacci connection is intrinsic: Fibonacci numbers F_n have Binet form F_n = (φ^n − ψ^n)/√5, with φ = (1+√5)/2 ≈ 1.618, ψ = (1−√5)/2 ≈ −0.618. The abc conjecture's radical function rad(abc) is multiplicative — a lattice-like structure over primes, but no crystallographic symmetry is invoked. | DEPTH: 6 — The abc conjecture is profound Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com