Show that the rational part of 2((1+sqrt(5))/2)^n is an integer - MathOverflow [closed] most recent 30 from http://mathoverflow.net 2013-05-24T07:01:27Z http://mathoverflow.net/feeds/question/56776 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/56776/show-that-the-rational-part-of-21sqrt5-2n-is-an-integer Show that the rational part of 2((1+sqrt(5))/2)^n is an integer L P 2011-02-27T00:08:16Z 2011-02-27T00:08:16Z <p>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.</p>