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small corrections, mainly the use of TeX
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edit approved Feb 1, 2014 at 11:52
Wlodek Kuperberg
edit approved Feb 1, 2014 at 11:52
Wlodek Kuperberg
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Does there exist a real number A$a$ such that the numbers \Sqrt{n^2 + A^2}$\sqrt{n^2 + a^2}$ (for all natural n$n$) are linearly independent over the field of rational numbers? It is evident that A$a$ cannot be rational. Is it possible to prove independence for A = \Pi$a=\pi$?

Does there exist a real number A such that numbers \Sqrt{n^2 + A^2} (for all natural n) are linearly independent over field of rational numbers? It is evident that A cannot be rational. Is it possible to prove independence for A = \Pi?

Does there exist a real number $a$ such that the numbers $\sqrt{n^2 + a^2}$ (for all natural $n$) are linearly independent over the field of rational numbers? It is evident that $a$ cannot be rational. Is it possible to prove independence for $a=\pi$?

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Anton
Anton
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Linear independence of the square roots over Q

Does there exist a real number A such that numbers \Sqrt{n^2 + A^2} (for all natural n) are linearly independent over field of rational numbers? It is evident that A cannot be rational. Is it possible to prove independence for A = \Pi?