On the Lebesgue-Nagell equation $x^2-2=y^p$

Ethan Katz, Kyle Pratt

We investigate the Lebesgue--Nagell equation \begin{align*} x^2-2=y^p \end{align*} in integers $x,y,p$ with $p\ge 3$ an odd prime. A longstanding folklore conjecture asserts that…