On Fibonacci and Lucas sequences modulo a prime and primality testing
We prove two properties regarding the Fibonacci and Lucas Sequences modulo a prime and use these to generalize the well-known property p∣Fp−p5. We then discuss these results in the context of primality testing.
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| Format: | Article |
| Language: | English |
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Emerald Publishing
2018-01-01
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| Series: | Arab Journal of Mathematical Sciences |
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S1319516617300646 |
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doaj-88ad4ecba9f944d8aa60b67911542d362021-05-03T01:41:57ZengEmerald PublishingArab Journal of Mathematical Sciences1319-51662018-01-0124191510.1016/j.ajmsc.2017.06.002On Fibonacci and Lucas sequences modulo a prime and primality testingDorin Andrica0Vlad Crişan1Fawzi Al-Thukair2Department of Mathematics, “ Babeş-Bolyai” University, Cluj Napoca, Mihail Kogalniceanu Street 1, Cluj-Napoca, RomaniaDepartment of Mathematics, University of Göttingen, Bunsenstraße 3-5, Göttingen, GermanyDepartment of Mathematics, College of Science, King Saud University, P.O. Box 2455, Riyadh 11451, Saudi ArabiaWe prove two properties regarding the Fibonacci and Lucas Sequences modulo a prime and use these to generalize the well-known property p∣Fp−p5. We then discuss these results in the context of primality testing.http://www.sciencedirect.com/science/article/pii/S1319516617300646Fibonacci and Lucas sequencesLegendre symbol |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Dorin Andrica Vlad Crişan Fawzi Al-Thukair |
| spellingShingle |
Dorin Andrica Vlad Crişan Fawzi Al-Thukair On Fibonacci and Lucas sequences modulo a prime and primality testing Arab Journal of Mathematical Sciences Fibonacci and Lucas sequences Legendre symbol |
| author_facet |
Dorin Andrica Vlad Crişan Fawzi Al-Thukair |
| author_sort |
Dorin Andrica |
| title |
On Fibonacci and Lucas sequences modulo a prime and primality testing |
| title_short |
On Fibonacci and Lucas sequences modulo a prime and primality testing |
| title_full |
On Fibonacci and Lucas sequences modulo a prime and primality testing |
| title_fullStr |
On Fibonacci and Lucas sequences modulo a prime and primality testing |
| title_full_unstemmed |
On Fibonacci and Lucas sequences modulo a prime and primality testing |
| title_sort |
on fibonacci and lucas sequences modulo a prime and primality testing |
| publisher |
Emerald Publishing |
| series |
Arab Journal of Mathematical Sciences |
| issn |
1319-5166 |
| publishDate |
2018-01-01 |
| description |
We prove two properties regarding the Fibonacci and Lucas Sequences modulo a prime and use these to generalize the well-known property p∣Fp−p5. We then discuss these results in the context of primality testing. |
| topic |
Fibonacci and Lucas sequences Legendre symbol |
| url |
http://www.sciencedirect.com/science/article/pii/S1319516617300646 |
| work_keys_str_mv |
AT dorinandrica onfibonacciandlucassequencesmoduloaprimeandprimalitytesting AT vladcrisan onfibonacciandlucassequencesmoduloaprimeandprimalitytesting AT fawzialthukair onfibonacciandlucassequencesmoduloaprimeandprimalitytesting |
| _version_ |
1721485709439664128 |