Hey everyone I'm bit trouble with this problem. Any help is appreciated: f(n+2)=f(n)+(f(n+1))^2, f(0)=1, f(1)=2 Find: f(2009) mod 7?
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It's not very sophisticated, but some quick calculations show that the sequence mod 7 is periodic with period 10 (it goes 1, 2, 5, 6, 6, 0, 6, 1, 0, 1 and repeat), and so f(2009) mod 7 = f(9) mod 7 = 1.
Waldo, thank you very much.
Ps: I guess the reason is that there are 7x7 = 49 possibilities, and when repeated over a new cycle begins. Then repeat from step 10th.
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