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Math Help - Recurrence Relations

  1. #1
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    Recurrence Relations

    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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  2. #2
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    Re: Recurrence Relations

    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.
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  3. #3
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    Re: Recurrence Relations

    Waldo, thank you very much.
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  4. #4
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    Re: Recurrence Relations

    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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