
Re: Approximation to square roots
Posted:
Jan 16, 2014 9:43 PM


On Thu, 16 Jan 2014, luirotorres@gmail.com wrote:
> "For each N,there exists a rational x / y such that the difference x / y  > Sqr(N) is less than 1 / [2N^2.Sqr(N)]. x, y is a solution of Pell´s equation > x^2 + N.y^2 = 1 ".
That's not Pell's equation and requirs any such x,y to be complex or x = 1, y = 0.
Assume x^2  n.y^2 = 1 has real roots, x,y. Then a = x, b = y is a solution to that Pell equation. Thusly a/b  sqr n < 1/(2n^2 sqr n) as required.

