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 $x$?
Quadratic equation with coefficients from FLT
2
$\begingroup$
elementary-number-theory
-
0Start with finding those roots, with: $$x_{1,2}=\frac{-b^n\pm\sqrt{b^{2n}-4a^nc^n}}{2a^n}$$ – 2012-03-04
-
1Alternatively, I started to think of this problem as applying http://en.wikipedia.org/wiki/Rational_root_theorem – 2012-03-04