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

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William Elliot

Posts: 1,243
Registered: 1/8/12
Approximation to square roots
Posted: Jan 18, 2014 10:51 PM
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> > Is this a known theorem?
> > "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 ".

> Bert. The theorem about Pell´s equation and continued fractions is well
> known. But not the inequality I propose. Please write down your complete
> demonstration.

Could the inequality come of the know inequalities of the partial fractions?

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