Drexel dragonThe Math ForumDonate to the Math Forum



Search All of the Math Forum:

Views expressed in these public forums are not endorsed by Drexel University or The Math Forum.


Math Forum » Discussions » sci.math.* » sci.math.independent

Topic: Approximation to square roots
Replies: 7   Last Post: Jan 19, 2014 10:01 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
William Elliot

Posts: 1,551
Registered: 1/8/12
Re: Approximation to square roots
Posted: Jan 16, 2014 9:43 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

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.



Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© Drexel University 1994-2014. All Rights Reserved.
The Math Forum is a research and educational enterprise of the Drexel University School of Education.