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arXiv · 2204.01858

Stewart's Theorem revisited: suppressing the norm $\pm 1$ hypothesis

Haojie Hong
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Abstract

Let $\gamma$ be an algebraic number of degree $2$ and not a root of unity. In this note we show that there exists a prime ideal $\mathfrak{p}$ of $\mathbb{Q}(\gamma)$ satisfying $\nu_\mathfrak{p}(\gamma^n-1)\ge 1$, such that the rational prime $p$ underlying $\mathfrak{p}$ grows quicker than $n$.

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Haojie Hong. 2022-04-04. Stewart's Theorem revisited: suppressing the norm $\pm 1$ hypothesis. https://arxiv.org/abs/2204.01858

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