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Math Help - sequence of f_n

  1. #1
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    Question sequence of f_n

    Let a and b be odd positive integers.
    Define the sequence f_n by putting f_1=a, f_2=b, and by letting f_n for n>2 be the greatest odd divisor of f_(n-1) + f_(n-2).
    Show that f_n is constant for n sufficiently large and determine the eventual value as a function of a and b.

    Thank you very much.
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  2. #2
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    Quote Originally Posted by Jenny20 View Post
    Let a and b be odd positive integers.
    Define the sequence f_n by putting f_1=a, f_2=b, and by letting f_n for n>2 be the greatest odd divisor of f_(n-1) + f_(n-2).
    Show that f_n is constant for n sufficiently large and determine the eventual value as a function of a and b.

    Thank you very much.
    If a,b>0.
    I have already posted my version here.
    But it is not able to load yet.

    It will be,
    f(n)=a*u_n+b*u_{n-1}
    Where,
    u_n is the Fibonacci numbers
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  3. #3
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    Hi perfecthacker,

    Do I have to wait for long to see your version?
    Anyway, I will go to check it often.
    Thank you very much.
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  4. #4
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    Quote Originally Posted by Jenny20 View Post
    Hi perfecthacker,

    Do I have to wait for long to see your version?
    I do not know there is some problem with the equation software.
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  5. #5
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    I see.
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