Let $x$ be $\cos \displaystyle \frac {2\pi} {n}$ for some natural number $n$. Then is there an integer $n$ such that $\mathbb{Q}(x^2+x)\neq \mathbb{Q}(x)$? I also would like to know if there is some known algorithm or computer program to find such $n$.
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closed as off topic by David Speyer, Will Sawin, Franz Lemmermeyer, David Loeffler, Qiaochu Yuan Sep 24 '12 at 21:07
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