# Thread: How does one solve a quadratic Diophantine equation?

1. ## How does one solve a quadratic Diophantine equation?

$
x^2 - Dy^2 = 1
$

For D = 2, x = 3 and y = 2.

What is the best way to go about solving an equation like this, where D is a known value, and x and y are variables?

Thanks,
Patrick

2. Originally Posted by PatrickFoster
$
x^2 - Dy^2 = 1
$

For D = 2, x = 3 and y = 2.

What is the best way to go about solving an equation like this, where D is a known value, and x and y are variables?

Thanks,
Patrick
Google "Pell's equation" to learn a little about these equations, which in general have no trivial solution and require some thorough knowledge of some rather nice quadratic number fields and their integer rings.

Tonio