## Show that the rational part of 2((1+sqrt(5))/2)^n is an integer [closed]

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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Please read the FAQ for this site: mathoverflow.net/faq#whatnot – Yemon Choi Feb 27 2011 at 0:09
This definitely is a basic homework question! – Somnath Basu Feb 27 2011 at 0:11
Homework problem, and it's not even a question, more like an order. – Stanley Yao Xiao Feb 27 2011 at 0:12