Professor PETER STEVENHAGEN (Universiteit Leiden)

will speak on

How solvable is the negative Pell equation?

Time: 2:00PM
Date: Thu 28th March 2024
Location: E0.32 (beside Pi restaurant) [map]

Abstract: Solving the Pell equation x^2-dy^2=1 in positive integers x and y is a challenge
that, starting with the days of Archimedes, has come up repeatedly in mathematical history.
In algebraic number theory, the equation is usually coupled with its negative counterpart x^2-dy^2=-1.
Unlike the original equation, which admits infinitely many solutions for all non-square integers d>0,
the negative Pell equation is solvable for a much smaller, but still infinite subset of d’s.
The exact size of the set of such (squarefree) d is now known, thanks to the work of Koymans and Pagano.
This settles a conjecture of mine that goes back to 1992, and that I will explain.

(This talk is part of the UCD School of Mathematics and Statistics Colloquium series.)

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