Fibonacci

Question 1

Pisano Period

Answer 1

In number theory, the nth Pisano period, written as π(n), is the period with which the sequence of Fibonacci numbers taken modulo n repeats.

Question 2

Pisano Period features

Answer 2

• With the exception of π(2) = 3, the Pisano period π(n) is always even.
• if the modulo base is a Fibonacci number (≥ 3) with an even index, the period is twice the index and the cycle has two zeros. If the base is a Fibonacci number (≥ 5) with an odd index, the period is four times the index and the cycle has four zeros.