## 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 language | English (US) |
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Pages (from-to) | 31-49 |

Number of pages | 19 |

Journal | Periodica Mathematica Hungarica |

Volume | 25 |

Issue number | 1 |

DOIs | |

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)

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