Andreas Reinhart

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math.NT2024

A counterexample to the Conjecture of Ankeny, Artin and Chowla

Andreas Reinhart

Let $p$ be a prime number with $p \equiv 1 mod 4$ , let $ω = \frac{1 + p}{2}$ , let $ε > 1$ be the fundamental unit of $Z [ω]$ and let $x$ and $y$ be the unique non…

math.NT2024

On counterexamples to Mordell's Pellian Equation Conjecture and the AAC-Conjecture: a non-computer based approach

Andreas Reinhart

In this note, we discuss recently discovered counterexamples to Mordell's Pellian Equation Conjecture and the Ankeny-Artin-Chowla-Conjecture. We provide a verification of the count…

math.NT2024

A counterexample to the Pellian equation conjecture of Mordell

Andreas Reinhart

Let $d \geq 2$ be a squarefree integer, let $ω \in {d, \frac{1 + d}{2}}$ be such that $Z [ω]$ is the ring of algebraic integers of the real quadratic number field…