Diophantine Equations and Congruent Number Equation Solutions

2015/04/16 by Mamuka Meskhishvili, Meskhishvili, Mamuka
Mathematics · #11D25 #11D41 #11D72 #14G05 #14H52 #FOS: Mathematics #General Mathematics (math.GM) #math.GM #msc:11D25 #msc:11D41 #msc:11D72 #msc:14G05 #msc:14H52

paper · pdf · doi:10.48550/arxiv.1504.04584

arxiv created 2015/04/16 · arxiv updated 2015/04/20

Abstract

By using pairs of nontrivial rational solutions of congruent number equation C_N: y²=x³-N²x, 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: (p²± q²)²-a² =\square_1,2 ,
c²-(p²± q²)² =\square_1,2 ,
a²+(p²± q²)² =\square_1,2 ,
(p²± q²)²-a² =(r²± s²)².

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