Geodesic
On Sequences of Squares with Constant Second Differences
Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 481-491

Voir la notice de l'article provenant de la source Cambridge University Press

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.
DOI : 10.4153/CMB-2006-047-9
Mots-clés : 11B83, 11Y85, 11D09, sequence of squares, second difference, elliptic curve 
Browkin, J.; Brzeziński, J. On Sequences of Squares with Constant Second Differences. Canadian mathematical bulletin, Tome 49 (2006) no. 4, pp. 481-491. doi: 10.4153/CMB-2006-047-9
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[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

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