Seminar at SMU Delhi

August 13, 2014 (Wednesday) , 3:30 PM at Webinar
Speaker: Pranabesh Das, Indian Statistical Institute, Delhi
Title: On the Ramanujan-Nagell Equation
Abstract of Talk
In 1913 Ramanujan conjectured that the equation $x^2+7=2^n$, $n\in{\mathbb{N}}$ has solutions only when $n=3,4,5,7$ and $15$. This was proved by Norwegian mathematician Trygve Nagell in $1948$. Several mathematicians considered this equation in more generality. Equations of the form $x^2+D=y^n$, with fixed $D\in{\mathbb{Z}}$ and variables $x, y, n\in {\mathbb{N}}, n\geq 2$ are called \emph{Ramanujan-Nagell equations}. These equations has a rich history. In this talk we will consider a special case of this equation taking $D$ from an infinite family of integers. We will attempt to solve $x^2+D=y^n, n\geq 3$ where $D$ is an $S-$integer composed of $3, 5, 11$.