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Pisano Periods: A Comparison Study, Katherine Willrich
Pisano Periods: A Comparison Study, Katherine Willrich
Mathematics Senior Capstone Papers
The Pisano period, denoted π(n), is the period during which the Fibonacci sequence repeats after reducing the original sequence modulo n. More generally, one can similarly define Pisano periods for any linear recurrence sequence; in this paper we compare the Pisano periods of certain linear recurrence sequences with the Pisano periods of the Fibonacci sequence. We first construct recurrence sequences, defining the initial values as integers from 2 to 1000 and second values as 1. This paper discusses how the constructed sequences are related to the matrix M = [(first row) 1 1 (second row) 1 0] reduced modulo n. …