Pisano period

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Pisano period

Summary

The Pisano period is a number theory concept describing how Fibonacci numbers behave when you take them “modulo” a fixed number (i.e., you only keep the remainders after division). What’s surprising is that, no matter which modulus you choose, the resulting sequence of remainders always eventually falls into a repeating cycle. 
The length of this cycle is called the Pisano period, written as π(n), and it depends on the chosen number n. For example, when working modulo 10, the Fibonacci sequence’s last digits repeat every 60 terms. This idea helps mathematicians understand hidden structure and periodicity in seemingly chaotic sequences, and it connects Fibonacci numbers with deeper properties of modular arithmetic and algebraic structure. 

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