Integral solutions in arithmetic progression for y2=x3+k

J. B. Lee; W. Y. Vélez

doi:10.1007/BF02454382

Integral solutions in arithmetic progression for y²=x³+k

J. B. Lee, W. Y. Vélez

Mathematics

Research output: Contribution to journal › Article › peer-review

13 Scopus citations

Abstract

Integral solutions to y²=x³+k, where either the x's or the y's, or both, are in arithmetic progression are studied. When both the x's and the y's are in arithmetic progression, then this situation is completely solved. One set of solutions where the y'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 4 x's in arithmetic progression and we disprove Mohanty's Conjecture [8] by constructing infinitely many sets of solutions where there are 4, 5 and 6 y's in arithmetic progression.

Original language	English (US)
Pages (from-to)	31-49
Number of pages	19
Journal	Periodica Mathematica Hungarica
Volume	25
Issue number	1
DOIs	https://doi.org/10.1007/BF02454382
State	Published - Aug 1992

Keywords

Arithmetic progression
Diophantine equation
Integral solution
Mathematics subject classification numbers: 1991, Primary 11D
elliptic curve

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1007/BF02454382

Cite this

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KW - Diophantine equation

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