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Pisano period: Difference between revisions
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{{draft task}}
[[Category:Mathematics]]
The [[wp:Fibonacci_Number|Fibonacci sequence]] taken modulo 2 is a periodic sequence of period 3 : 0, 1, 1, 0, 1, 1, ...
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Prime numbers are straightforward; the Pisano period of a prime number '''p''' is simply: '''pisano(p)'''. The Pisano period of a composite number '''c''' may be found in different ways. It may be calculated directly: '''pisano(c)''', which works, but may be time consuming to find, especially for larger integers, or, it may be calculated by finding the [[wp:Least common multiple|least common multiple]] of the Pisano periods of each composite component.
E.G. Given a Pisano period function: pisano(x), and a least common multiple function lcm(x, y):▼
;E.G.:
'''pisano(m × n)''' is equivalent to '''lcm(pisano(m), pisano(n))''' where '''m''' and '''n''' are '''[[wp:Coprime|coprime]]'''
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The equation is conjectured, no exceptions have been seen.
If a positive integer '''i''' is split into its prime factors then the second and first equations above can be applied to generate the pisano period.
;Task
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Print pisano(m) for every integer from 1 to 180.
;Related tasks
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* [[Prime decomposition]]
* [[Least common multiple]]
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=={{header|Factor}}==
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