Solving Pell's Equation: From Archimedes to Lagrange

Reginald Lybbert

12:00, Friday, Feb. 21
BURN 1025



Number theorists have long been fascinated with Diophantine equations, i.e. algebraic equations with integer solutions. These problems often have very simple statements, but surprisingly deep solutions. One of the prominent Diophantine equations is the Pell equation, $x^2 - Ny^2 = 1$. This equation has shown up in applications ranging from finding rational approximations to square roots, to finding units in quadratic number fields.

In this talk, I will go over the history of this equation as well as a method for finding solutions, via continued fractions. I will also discuss an ancient number puzzle, known as the Archimedes's Cattle Problem, in which we count the number of cattle belonging to the sun god.

All graduate students are invited. As with all talks in the graduate student seminar, this talk will be accessible to all graduate students in math and stats.

This seminar was made possible by funding from the McGill mathematics and statistics department and PGSS.

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