Corpus ID: 118082838

Perfect Cuboid and Congruent Number Equation Solutions

@article{Meskhishvili2012PerfectCA,
  title={Perfect Cuboid and Congruent Number Equation Solutions},
  author={Mamuka Meskhishvili},
  journal={arXiv: Number Theory},
  year={2012}
}
  • Mamuka Meskhishvili
  • Published 2012
  • Mathematics
  • arXiv: Number Theory
  • A perfect cuboid (PC) is a rectangular parallelepiped with rational sides $a,b,c$ whose face diagonals $d_{ab}$, $d_{bc}$, $d_{ac}$ and space (body) diagonal $d_s$ are rationals. The existence or otherwise of PC is a problem known since at least the time of Leonhard Euler. This research establishes equivalent conditions of PC by nontrivial rational solutions $(X,Y)$} and $(Z,W)$} of congruent number equation $ y^2=x^3-N^2x$, where product $XZ$ is a square. By using such pair of solutions five… CONTINUE READING
    Diophantine Equations and Congruent Number Equation Solutions

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