Pisano period

Pisano period

In mathematics, the "n"th Pisano period, written π("n"), is the period with which the sequence of Fibonacci numbers, modulo "n" repeats. For example, the Fibonacci numbers mod 3 are num|0, 1, 1, 2, 0, 2, 2, 1, 0, 1, 1, etc., with the first eight numbers repeating, so π(3) = 8.

The first Pisano periods (sequence in OEIS) and their cycles (with spaces before the zeros for readability) are:

Term

Pisano periods are named after Leonardo Pisano, better known as Fibonacci.

References

* [http://maths.dur.ac.uk/~dma0rcj/PED/fib.pdf Matrix methods for Fibonacci and related sequences]

External links

* [http://www.math.temple.edu/~renault/fibonacci/fiblist.html Table of Pisano periods]
* [http://mathworld.wolfram.com/PisanoPeriod.html Mathworld article on Pisano periods]


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