Rational solution
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
I don't understand.Explain it.
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- Tahmid Hasan
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Re: Rational solution
Sanzeed are you meaning $\sqrt {n-1} + \sqrt {n+1}$ is rational
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- nafistiham
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Re: Rational solution
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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Re: Rational solution
Yes, my solution says so.But i wanna match it with you two.Please post the solution.
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- Phlembac Adib Hasan
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Re: Rational solution
Just contradiction.Let it as rational.then square both sides.The result is obvious.
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Re: Rational solution
Thanks a lot.
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