manuscripta mathematica

, Volume 80, Issue 1, pp 373–392

Explicit complete solution in integers of a class of equations (ax2 -b )(ay2 -b) =z2 -c

  • Kenji Kashihara

DOI: 10.1007/BF03026559

Cite this article as:
Kashihara, K. Manuscripta Math (1993) 80: 373. doi:10.1007/BF03026559


In this paper we will study the equation for arbitrary integersa ≠ 0,c andb = ±1, ±2 or ±4 Whenb = ±4, we suppose c is divisible by 4. The paper will provide one with a method for finding algorithmically all integral non-trivial solutions of the title equations, where an explicit unit of\(Q(\sqrt {a^2 n^2 - ab} )\) plays an important role.

Copyright information

© Springer-Verlag 1993

Authors and Affiliations

  • Kenji Kashihara
    • 1
  1. 1.Department of MathematicsAnan College of TechnologyAnan-shi TokushimaJapan