Theoretical Statistics and Mathematics Unit, ISI 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
$3, 5, 11$.