A counterexample to the Conjecture of Ankeny, Artin and Chowla

2024/10/29 by Reinhart, Andreas · 2 citations
#11R11 #11R27 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2410.21864

Abstract

Let p be a prime number with p≡ 1\mod 4, let ω=(1+√(p))/(2), let ε>1 be the fundamental unit of ℤ[ω] and let x and y be the unique nonnegative integers with ε=x+yω. The Ankeny-Artin-Chowla-Conjecture states that p is not a divisor of y. In this note, we provide and discuss a counterexample to this conjecture.

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• Wieferich primes in number fields and the conjectures of Ankeny--Artin--Chowla and Mordell
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