# 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} }

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

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