Rational solution

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SANZEED
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Rational solution

Unread post by SANZEED » Sun Jan 22, 2012 6:22 am

Is there a positive integer $n$ such that the sum of the square roots of the adjacent integers of$n$ is rational.
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Phlembac Adib Hasan
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Re: Rational solution

Unread post by Phlembac Adib Hasan » Sun Jan 22, 2012 9:22 am

I don't understand.Explain it.
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Tahmid Hasan
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Re: Rational solution

Unread post by Tahmid Hasan » Sun Jan 22, 2012 10:22 am

Sanzeed are you meaning $\sqrt {n-1} + \sqrt {n+1}$ is rational
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Re: Rational solution

Unread post by nafistiham » Sun Jan 22, 2012 5:33 pm

If tahmid is right then there is no such integer. we can prove that using the text book way.
\[\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0\]
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SANZEED
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Re: Rational solution

Unread post by SANZEED » Wed Jan 25, 2012 12:08 am

Yes, my solution says so.But i wanna match it with you two.Please post the solution.
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Re: Rational solution

Unread post by Phlembac Adib Hasan » Wed Jan 25, 2012 10:26 am

Just contradiction.Let it as rational.then square both sides.The result is obvious.
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SANZEED
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Re: Rational solution

Unread post by SANZEED » Tue Jan 31, 2012 11:42 pm

Thanks a lot.
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