Hostname: page-component-586b7cd67f-t7fkt Total loading time: 0 Render date: 2024-11-22T05:13:41.211Z Has data issue: false hasContentIssue false
  • English
  • Français

On Sequences of Squares with Constant Second Differences

Published online by Cambridge University Press:  20 November 2018

J. Browkin  and
J. Brzeziński
J. Browkin
Affiliation:
Institute of Mathematics, University of Warsaw, ul. Banacha 2, PL-02-097 Warsaw, Poland e-mail: [email protected]
J. Brzeziński
Affiliation:
Department of Mathematics, Chalmers University of Technology, and Göteborg University, S-41296 Göteborg, Sweden e-mail: [email protected]
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The aim of this paper is to study sequences of integers for which the second differences between their squares are constant. We show that there are infinitely many nontrivial monotone sextuples having this property and discuss some related problems.

Keywords

11B8311Y8511D09sequence of squaressecond differenceelliptic curve
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 49 , Issue 4 , 01 December 2006 , pp. 481 - 491
Copyright
Copyright © Canadian Mathematical Society 2006

References

[A] Allison, D., On square values of quadratics. Math. Proc. Camb. Philos. Soc. 99(1986), no. 3, 381–383.Google Scholar
[Ba] Barbeau, E. J., Numbers differing from consecutive squares by squares. Canad. Math. Bull. 28(1985), no. 3, 337–342.Google Scholar
[Br] Bremner, A., On square values of quadratics. Acta Arith. 108(2003), no. 2, 95–111.Google Scholar
[Bu] Buell, D. A., Integer squares with constant second difference. Math. Comp. 49(1987), 635–644.Google Scholar
[L] Lipshitz, L., Quadratic forms, the five square problem, and diophantine equations. In: The Collected Works of J. Richard Büchi (MacLane, S. and Siefkes, Dirk, eds.), Springer, 1990, 677–680.Google Scholar
[P] Pinch, R. G. E., Squares in quadratic progressions. Math. Comp. 60(1993), 841–845.Google Scholar
[ST] Silverman, J. H. and Tate, J., Rational Points on Elliptic Curves. Undergraduate Texts in Mathematics, Springer-Verlag, Berlin, 1992.Google Scholar
[V] Vojta, P., Diagonal quadratic forms and Hilbert's tenth problem. In: Hilberts Tenth Problem, Contemp. Math. 270, American Mathematics Society, Providence, RI, 2000, pp. 261–274.Google Scholar
[Y] Yamagishi, H., On the solutions of certain quadratic equations and Lang's conjecture. Acta Arith. 109(2003), no. 2, 159–168.Google Scholar