# Dr. Mamuka Meskhishvili - Georgian-American High School

## Contact Details

NameDr. Mamuka Meskhishvili |
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PrefixDr. |
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Degree(s)PhD |
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TitleDirector |
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AffiliationGeorgian-American High School |
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CityTbilisi |
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CountryGeorgia |
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SpecialtiesMathematics |
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## Pubs By Year |
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## Pub CategoriesMathematics - Number Theory (4) Mathematics - General Mathematics (2) |

## Publications Authored By Dr. Mamuka Meskhishvili

By using pairs of nontrivial rational solutions of congruent number equation $$ C_N:\;\;y^2=x^3-N^2x, $$ constructed are pairs of rational right (Pythagorean) triangles with one common side and the other sides equal to the sum and difference of the squares of the same rational numbers. The parametrizations are found for following Diophantine systems: \begin{align*} (p^2\pm q^2)^2-a^2 & =\square_{1,2}\,, \\[0.2cm] c^2-(p^2\pm q^2)^2 & =\square_{1,2}\,, \\[0. Read More

We consider nearly-perfect cuboids (NPC), where the only irrational is one of the face diagonals. Obtained are three rational parametrizations for NPC with one parameter. Read More

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. Read More