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Glorfindel
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I found that the square root of any prime number S can be approximated, at the n-th order, as a rational number represented by the polynomials shown below. x_0$x_0$ is an initial seed, which is a rational number chosen “close” to \sqrt{S}$\sqrt S$. I used the iterative method, not the continued fractions

enter image description here

My question: Is someone aware of this result? Is it already known and has been published elsewhere? If affirmative, please post the reference!

I found that the square root of any prime number S can be approximated, at the n-th order, as a rational number represented by the polynomials shown below. x_0 is an initial seed, which is a rational number chosen “close” to \sqrt{S}. I used the iterative method, not the continued fractions

enter image description here

My question: Is someone aware of this result? Is it already known and has been published elsewhere? If affirmative, please post the reference!

I found that the square root of any prime number S can be approximated, at the n-th order, as a rational number represented by the polynomials shown below. $x_0$ is an initial seed, which is a rational number chosen “close” to $\sqrt S$. I used the iterative method, not the continued fractions

enter image description here

My question: Is someone aware of this result? Is it already known and has been published elsewhere? If affirmative, please post the reference!

I found that the square root of any prime number S can be approximated, at the n-th order, as a rational number represented by the polynomials shown below. x_0 is an initial seed, which is a rational number chosen “close” to \sqrt{S}. I used the iterative method, not the continued fractions   

Derived expressionenter image description here

My question: Is someone aware of this result? Is it already known and has been published elsewhere? If affirmative, please post the reference!

I found that the square root of any prime number S can be approximated, at the n-th order, as a rational number represented by the polynomials shown below. x_0 is an initial seed, which is a rational number chosen “close” to \sqrt{S}. I used the iterative method, not the continued fractions  Derived expression

My question: Is someone aware of this result? Is it already known and has been published elsewhere? If affirmative, please post the reference!

I found that the square root of any prime number S can be approximated, at the n-th order, as a rational number represented by the polynomials shown below. x_0 is an initial seed, which is a rational number chosen “close” to \sqrt{S}. I used the iterative method, not the continued fractions 

enter image description here

My question: Is someone aware of this result? Is it already known and has been published elsewhere? If affirmative, please post the reference!

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Square root of prime numbers

I found that the square root of any prime number S can be approximated, at the n-th order, as a rational number represented by the polynomials shown below. x_0 is an initial seed, which is a rational number chosen “close” to \sqrt{S}. I used the iterative method, not the continued fractions Derived expression

My question: Is someone aware of this result? Is it already known and has been published elsewhere? If affirmative, please post the reference!