Solving the Fundamental Equation \(y^{{\tau}(r)} = y\) in \(\mathbb{Z}_r\)

In this short note, we aim to provide a compact formula for the smallest odd integer \(\tau(r) > 1\) such that the fixed-point equation \(y^{\tau(r)} = y\) has the maximal set of solutions in the commutative ring of \(r\)-adic integers.

Authors

Publication Details

Journal
Zenodo (CERN European Organization for Nuclear Research)
Published
2025-12-22
DOI
https://doi.org/10.5281/zenodo.18023892
Primary Topic
advanced mathematical theories
Type
article
Field-Weighted Citation Impact
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article

Solving the Fundamental Equation \(y^{{\tau}(r)} = y\) in \(\mathbb{Z}_r\)

Marco Ripà
Zenodo (CERN European Organization for Nuclear Research)
advanced mathematical theories
article

Solving the Fundamental Equation \(y^{{\tau}(r)} = y\) in \(\mathbb{Z}_r\)

Marco Ripà
article en

Abstract

In this short note, we aim to provide a compact formula for the smallest odd integer \(\tau(r) > 1\) such that the fixed-point equation \(y^{\tau(r)} = y\) has the maximal set of solutions in the commutative ring of \(r\)-adic integers.

Zenodo (CERN European Organization for Nuclear Research)
Openalex Percentile: Top 23%
advanced mathematical theories
DOIOpen Access PDFOpenAlex
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Solving the Fundamental Equation \(y^{{\tau}(r)} = y\) in \(\mathbb{Z}_r\) — Marco Ripà · Zenodo (CERN European Organization for Nuclear Research) (2025) | TGRS Research Map | TGRS