ABC Conjecture Verification Links Wall's Conjecture to Infinite Non-Fibonacci-Wieferich Primes — E8 Intelligence Research

FINDING: ABC conjecture remains unverified; LANA project attempts formal verification of Mochizuki's proof; Wall's conjecture linked to abc implies infinite non-Fibonacci-Wieferich primes. | MATH: ABC conjecture: For any ε > 0, there exists C(ε) such that for all coprime integers a, b, c with a + b = c, max(|a|,|b|,|c|) < C(ε) * rad(abc)^(1+ε), where rad(n) = product of distinct primes dividing n. Wall's conjecture: For prime p, F_{p - (p/5)} ≡ 0 mod p (Fibonacci-Wieferich primes satisfy F_{p - (p/5)} ≡ 0 mod p^2). Implication: abc → infinitely many primes p where F_{p - (p/5)} ≡ 0 mod p but not mod p^2. | CONNECTION: No direct geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry) found. The Fibonacci connection involves golden ratio (φ = 1.618...) via Binet formula, but the result is about prime divisibility, not geometric ratios. | DEPTH: 4 — The abc conjecture is profound for number theory (links prime factorization to addition), but the verificat Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

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Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2026-08-17
DOI
https://doi.org/10.5281/zenodo.21974005
Primary Topic
Analytic Number Theory Research
Type
preprint
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preprint

ABC Conjecture Verification Links Wall's Conjecture to Infinite Non-Fibonacci-Wieferich Primes — E8 Intelligence Research

Andrew Stewart Caldin
Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
preprint

ABC Conjecture Verification Links Wall's Conjecture to Infinite Non-Fibonacci-Wieferich Primes — E8 Intelligence Research

Andrew Stewart Caldin
preprint en

Abstract

FINDING: ABC conjecture remains unverified; LANA project attempts formal verification of Mochizuki's proof; Wall's conjecture linked to abc implies infinite non-Fibonacci-Wieferich primes. | MATH: ABC conjecture: For any ε > 0, there exists C(ε) such that for all coprime integers a, b, c with a + b = c, max(|a|,|b|,|c|) < C(ε) * rad(abc)^(1+ε), where rad(n) = product of distinct primes dividing n. Wall's conjecture: For prime p, F_{p - (p/5)} ≡ 0 mod p (Fibonacci-Wieferich primes satisfy F_{p - (p/5)} ≡ 0 mod p^2). Implication: abc → infinitely many primes p where F_{p - (p/5)} ≡ 0 mod p but not mod p^2. | CONNECTION: No direct geometric harmony (0.382, 0.618, 0.786, 1.618, 2.618, base-60, crystallographic symmetry) found. The Fibonacci connection involves golden ratio (φ = 1.618...) via Binet formula, but the result is about prime divisibility, not geometric ratios. | DEPTH: 4 — The abc conjecture is profound for number theory (links prime factorization to addition), but the verificat Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com

Zenodo (CERN European Organization for Nuclear Research)
Analytic Number Theory Research
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