Squares with three nonzero digits

Michael A. Bennett; Adrian Maria Scheerer

doi:10.1007/978-3-319-55357-3_4

Squares with three nonzero digits

Michael A. Bennett^*, Adrian Maria Scheerer

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Analysis und Zahlentheorie (5010)

Publikation: Beitrag in Buch/Bericht/Konferenzband › Beitrag in Buch/Bericht › Begutachtung

Abstract

We determine all integers n such that n² has at most three base-q digits for q ε (2, 3, 4, 5, 8, 16). More generally, we show that all solutions to equations of the shape where q is an odd prime, n > m > 0 and t², πMπ,N < q, either arise from "obvious" polynomial families or satisfy m ≤ 3. Our arguments rely upon Padé approximants to the binomial function, considered q-adically.

Originalsprache	englisch
Titel	Number Theory - Diophantine Problems, Uniform Distribution and Applications
Untertitel	Festschrift in Honour of Robert F. Tichy's 60th Birthday
Herausgeber (Verlag)	Springer International Publishing AG
Seiten	83-108
Seitenumfang	26
ISBN (elektronisch)	9783319553573
ISBN (Print)	9783319553566
DOIs	https://doi.org/10.1007/978-3-319-55357-3_4
Publikationsstatus	Veröffentlicht - 1 Juni 2017

ASJC Scopus subject areas

Allgemeine Mathematik

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10.1007/978-3-319-55357-3_4

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http://www.scopus.com/inward/record.url?scp=85033694744&partnerID=8YFLogxK

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AB - We determine all integers n such that n2 has at most three base-q digits for q ε (2, 3, 4, 5, 8, 16). More generally, we show that all solutions to equations of the shape where q is an odd prime, n > m > 0 and t2, πMπ,N < q, either arise from "obvious" polynomial families or satisfy m ≤ 3. Our arguments rely upon Padé approximants to the binomial function, considered q-adically.

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BT - Number Theory - Diophantine Problems, Uniform Distribution and Applications

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ER -

Squares with three nonzero digits

Abstract

ASJC Scopus subject areas

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