Example
As an example, consider the instance of Pell's equation for n = 7; that is,
The sequence of convergents for the square root of seven are
-
h / k (Convergent) h2 −7k2 (Pell-type approximation) 2 / 1 −3 3 / 1 +2 5 / 2 −3 8 / 3 +1
Therefore, the fundamental solution is formed by the pair (8, 3). Applying the recurrence formula to this solution generates the infinite sequence of solutions
- (8, 3); (127, 48); (2024, 765); (32257, 12192); (514088, 194307); (8193151; 3096720); (130576328, 49353213); ...
Read more about this topic: Pell's Equation
Famous quotes containing the word example:
“Our intellect is not the most subtle, the most powerful, the most appropriate, instrument for revealing the truth. It is life that, little by little, example by example, permits us to see that what is most important to our heart, or to our mind, is learned not by reasoning but through other agencies. Then it is that the intellect, observing their superiority, abdicates its control to them upon reasoned grounds and agrees to become their collaborator and lackey.”
—Marcel Proust (1871–1922)