If $2(\frac{1+\sqrt{5}}{2})^n $ for a positive integer $n$ is equal to $a + b\sqrt{5}$ for rationals $a$ and $b$, show that $a$ is an integer.
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closed as too localized by Andres Caicedo, Yemon Choi, Qiaochu Yuan, Steve Huntsman, HW Feb 27 2011 at 0:19 |
