New class of solutions of the diophantine equations

Abstract

The thesis entitled A New class of solutions of the Diophantine Equations consists of ten chapters and the same has been analyzed intensively for the purpose of upcoming Mathematical society The first part starts with introduction of the study, followed by objectives of research review of literature and ends with organization of the research newlineThe second part presents different patterns of non-zero integral points on the hyperbola and#1050452;and#1051446; and#1051974; 6and#1050452;and#1050453; + and#1050453;and#1051446; +6and#1050452; and#1051974; 2and#1050453;+5 = 0.Some research efforts are also devoted to explore remarkable relations among the solutions In the third part analyses two interesting ternary quadratic equations in three variables newline(i) x2 6xy + y 2+6x 2y +5 = Z2+4 newline(ii) 7x2 18xy +7y 2+10x 6y +2 = Z2+1 newlinefor determining its infinitely many nonzero integral solutions. Also a few interesting relations among the solutions for particular cases have been presented. newline newline