Erik Bergström Björlund: Diofantiska ekvationer

Abstract:

A diophantine equation is an equation where only integer solutions are sought after. The pythagorean equation, \(x ^2 + y^ 2 = z^ 2 \), is a type of diophantine equation where we can find three integers x, y, z that solves the equation. These numbers are called pythagorean triples. An example of a diphantine equation is the Pell equation, \(x ^2−ny^2 = 1\). The equation has a special connection to the irrational number \(\sqrt{2} \), and we will also find a method for generating an infinite number of solutions to the equation.