I would appreciate if somebody could help me with the following problem
If $\{a_n\}$ satisfy: $$a_1=a_2=1$$ $$a_{n+2}=a_{n+1}+a_{n}$$ How to find the remainder of $\dfrac{a_{2011}}{5}$
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2See http://math.stackexchange.com/questions/60340/fibonacci-modular-results – lab bhattacharjee Nov 01 '14 at 04:54
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1Also, you can adjust the values of $m,n$ in http://math.stackexchange.com/questions/11477/showing-that-an-equation-holds-true-with-a-fibonacci-sequence-f-nm-f-n-1?lq=1 using $5\mid F_{5n}$ – lab bhattacharjee Nov 01 '14 at 04:58