 
Summary: Pell Equations
Putnam Practice
November 17, 2004
A famous example of a Diophantine equation is Pell equation. It is an
equation of the form
x2
 Dy2
= 1
with D a positive integer that is not a perfect square. To find all positive
integer solutions of this equation, one first determines a minimal solution
(i.e. the solution (x0, y0) for which x0+y0
D is minimal). There is a general
way to compute this minimal solution, however, in all problems below the
minimal solution is easy to guess.
The other solutions are given by
xn + yn
D = (x0 + y0
