Abstract of Talk
We describe a general approach for solving polynomial diophantine equations $
f(x_1,\,x_2,\,\ldots,\,x_n)=0$
where $f(x_1,\,x_2,\,\ldots,\,x_n)$ is a quartic or higher degree form, with integer coefficients, in four or more independent variables $x_1,\,x_2,\,\ldots,\,x_n$. The general approach is also applicable to simultaneous diophantine equations $
f_j(x_1,\,x_2,\,\ldots,\,x_{n})=0,\;j=1,\,2,\,\ldots,\,r,$
where $f_j(x_i)$ are forms, with integer coefficients, in the $n$ independent variables $x_1,\,x_2,\,\ldots,\,x_{n}$ with $ n$ being $ \geq 5$. We give several examples of specific diophantine equations and diophantine systems that can be solved by following the aforementioned general approach.