Exploring Solutions of Certain Diophantine Equations

Abstract

Diophantus of Alexandra (c. 200 – 284 A.D.), usually addressed as the ‘father of algebra’, is best known for his book Arithmetica, a work on the solution of algebraic equations and the theory. The study of Diophantine equations involves interplay among number theory, calculus, combinatorics, algebra and geometry. The solution in integers of algebraic equations, in more than one unknown with integral coefficients, is one of the most challenging problems in the theory of numbers. The celebrated authors like Diophantus, Brahmagupta (c. 598 – 668 A.D.), Bhaskaracharya II (1114 – 1185 A.D.), P. Fermat (1601 – 1665 A.D.), L. Euler (1707 – 1783 A.D.), J.L. Lagrange (1736 – 1813 A.D.), C.F. Gauss (1777 – 1855 A.D.) and many others paid attention to such problems.