Show that the following expression/sequence is alternately even or odd!

$\displaystyle \lfloor(\sqrt2+1)^n\rfloor$

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- Nov 24th 2010, 09:15 AMzadirParity of an expression
Show that the following expression/sequence is alternately even or odd!

$\displaystyle \lfloor(\sqrt2+1)^n\rfloor$ - Nov 24th 2010, 12:44 PMOpalg
Hint: Show that $\displaystyle (1+\sqrt2)^n + (1-\sqrt2)^n$ is an integer.