In my study I understand that the Fibonacci sequence mod $k$ is periodic, with period less than $k^2$. Can any one generalize this with good proof?
Fibonacci modular results 2
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fibonacci-numbers
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0Thank you for all mathematicians, who given the comments and suggestions. I got and understand this question by JYRKI LAHTONEN. Thank you so much for all. – 2011-08-31
1 Answers
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HINT $ $ If you consider an n'th order linear recurrence in "system form", i.e. as a shift map on n-tuples then the periodicity is obvious, being cycles of a permutation on a finite set. See my comments about reinventing the wheel (cycle) in this answer and this one.
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0yes sir. I got it! thank you. – 2011-08-31