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Integral solutions in arithmetic progression for y2=x3+k (1992)

Lee, J. -B. ; Vélez, W. Y.

Springer

Periodica mathematica Hungarica 25 (1992), S. 31-49

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ISSN: 1588-2829

Keywords: 1991 ; Primary 11D ; Integral solution ; Arithmetic progression ; elliptic curve ; Diophantine equation

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics

Notes: Abstract Integral solutions toy 2=x 3+k, where either thex's or they's, or both, are in arithmetic progression are studied. When both thex's and they's are in arithmetic progression, then this situation is completely solved. One set of solutions where they's formed an arithmetic progression of length 4 had already been constructed. In this paper, we construct infinitely many sets of solutions where there are 4x's in arithmetic progression and we disprove Mohanty's Conjecture [8] by constructing infinitely many sets of solutions where there are 4, 5 and 6y's in arithmetic progression.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02454382

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