Squares with three nonzero digits

Michael A. Bennett*, Adrian Maria Scheerer

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review


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.

Original languageEnglish
Title of host publicationNumber Theory - Diophantine Problems, Uniform Distribution and Applications
Subtitle of host publicationFestschrift in Honour of Robert F. Tichy's 60th Birthday
PublisherSpringer International Publishing AG
Number of pages26
ISBN (Electronic)9783319553573
ISBN (Print)9783319553566
Publication statusPublished - 1 Jun 2017

ASJC Scopus subject areas

  • Mathematics(all)

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