Integral solutions in arithmetic progression for y2=x3+k

J. B. Lee, W. Y. Vélez

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

Integral solutions to y 2=x 3+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 languageEnglish (US)
Pages (from-to)31-49
Number of pages19
JournalPeriodica Mathematica Hungarica
Volume25
Issue number1
DOIs
StatePublished - Aug 1 1992

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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