Seminar at SMU Delhi

November 20, 2018 (Tuesday) , 3:30 PM at Webinar
Speaker: Ajai Choudhry, HRI Allahabad
Title: Quartic and higher degree diophantine equations
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.