Squares with Three Nonzero Digits

Michael A. Bennett () and Adrian-Maria Scheerer ()
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Michael A. Bennett: University of British Columbia, Department of Mathematics
Adrian-Maria Scheerer: Graz University of Technology, Institute of Analysis and Number Theory

A chapter in Number Theory – Diophantine Problems, Uniform Distribution and Applications, 2017, pp 83-108 from Springer

Abstract: Abstract We determine all integers n such that n 2 has at most three base-q digits for q ∈ {2, 3, 4, 5, 8, 16}. More generally, we show that all solutions to equations of the shape Y 2 = t 2 + M ⋅ q m + N ⋅ q n , $$\displaystyle{Y ^{2} = t^{2} + M \cdot q^{m} + N \cdot q^{n},}$$ where q is an odd prime, n > m > 0 and t 2, | M |, N

Keywords: Primary 11D61; Secondary 11A63; 11J25 (search for similar items in EconPapers)
Date: 2017
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-55357-3_4

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

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