Editing Fibonacci sequence (section)

=== Periodicity modulo ''n'' ===
{{Main|Pisano period}}

If the members of the Fibonacci sequence are taken mod&nbsp;{{mvar|n}}, the resulting sequence is [[periodic sequence|periodic]] with period at most&nbsp;{{math|6''n''}}.<ref>{{Citation | title = Problems and Solutions: Solutions: E3410 | last1 = Freyd | first1 = Peter | last2 = Brown | first2 = Kevin S. | journal = The American Mathematical Monthly | volume = 99 | issue = 3 | pages = 278–79 |date= 1993 | doi=10.2307/2325076| jstor = 2325076 }}</ref> The lengths of the periods for various {{mvar|n}} form the so-called [[Pisano period]]s.<ref>{{Cite OEIS|1=A001175|2=Pisano periods (or Pisano numbers): period of Fibonacci numbers mod n|mode=cs2}}</ref> Determining a general formula for the Pisano periods is an [[open problem]], which includes as a subproblem a special instance of the problem of finding the [[multiplicative order]] of a [[modular arithmetic|modular integer]] or of an element in a [[finite field]]. However, for any particular {{mvar|n}}, the Pisano period may be found as an instance of [[cycle detection]].