I have made some observation on very interesting material on Fibonacci series. I need some help in proving them mathematically.
We can observe that the periodicity of Fibonacci numbers modulo m, which non-trivial. Can we prove this mathematically? Also, how we can prove this period is always an even and the period itself modulo m is less than or equal to m2−1. How we prove this one. Also, justify mathematically the period modulo m is less than or equal to 6m, and other interesting facts about the period modulo a prime number.
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