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Let $a,b,c>0$ be pairwise relatively prime and $n>2$ be odd. Can the equation, $a^n\cdot x^2+b^n\cdot x+c^n=0$, have rational roots $x$?

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    Start with finding those roots, with: $$x_{1,2}=\frac{-b^n\pm\sqrt{b^{2n}-4a^nc^n}}{2a^n}$$2012-03-04
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    Alternatively, I started to think of this problem as applying http://en.wikipedia.org/wiki/Rational_root_theorem2012-03-04

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