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The Period and Rank of the Complex-type Padovan-p Numbers Modulo m

Year 2021, Volume: 6 Issue: 3, 156 - 161, 30.12.2021

Abstract

In this paper, we study the complex-type Padovan-p sequence modulo m and then we give
some results concerning the periods and the ranks of these sequences for any p and m. Furthermore, we
produce the cyclic groups using the multiplicative orders of the generating matrices of the complex-type
Padovan-p sequences when read modulo m. Finally, we give the relationships between the periods of the
complex-type Padovan-p sequences modulo m and the orders of the cyclic groups produced.

References

  • Akuzum Y, Deveci O. The Hadamard-type k-step Fibonacci sequences in groups. Communications in Algebra. 48(7), 2020, 2844−2856.
  • Aydin H, Dikici R. General Fibonacci sequences in finite groups. Fibonacci Quarterly. 36(3), 1998, 216−221.
  • Campbell CM, Doostie H, Robertson EF. Fibonacci length of generating pairs in groups. In: Bergum, G. E., ed. Applications of Fibonacci Numbers. Vol. 3. Springer, Dordrecht: Kluwer Academic Publishers, 1990, pp. 27−35.
  • Deveci O, Karaduman E. On the Padovan p-numbers. Hacettepe Journal of Mathematics and Statistics. 46(4), 2017, 579−592.
  • Deveci O, Akuzum Y, Karaduman E. The Pell-Padovan p-Sequences and Its Applications. Utilitas Mathematica. 98, 2015, 327−347.
  • Deveci O, Akuzum Y. The Cyclic Groups and The Semigroups via MacWilliams and Chebyshev Matrices. Journal of Mathematics Research. 6(2), 2014, 55−58.
  • Deveci O, Shannon AG. The complex-type k-Fibonacci sequences and their applications. Communications in Algebra. 49(3), 2021, 1352−1367.
  • Doostie H, Hashemi M. Fibonacci lengths involving the Wall number K(n). Journal of Applied Mathematics and Computing. 20(1-2), 2006, 171−180.
  • Erdag O, Halıcı S, Deveci O. The Complex-Type Padovan-p Sequences. is submitted.
  • Falcon S, Plaza A. k-Fibonacci sequences modulo m. Chaos, Solitons and Fractals. 41(1), 2009, 497−504.
  • Karaduman E, Aydın H. k-nacci sequences in some special groups of finite order. Mathematical and Computer Modelling. 50(1-2), 2009, 53−58.
  • Knox SW. Fibonacci sequences in finite groups, Fibonacci Quarterly. 30(2), 1992, 116−120.
  • Lu K, Wang J. k-step Fibonacci sequence modulo m. Utilitas Mathematica. 71, 2006, 169−177.
  • Ozkan E, Aydin H, Dikici R. 3-step Fibonacci series modulo m. Applied Mathematics and Computation. 143(1), 2003, 165−172.
  • Wall DD. Fibonacci series modulo m, American Mathematical Monthly. 67(6), 1960, 525−532.
  • Wilcox HJ. Fibonacci sequences of period n in Groups. Fibonacci Quarterly. 24(4), 1986, 356−361.
Year 2021, Volume: 6 Issue: 3, 156 - 161, 30.12.2021

Abstract

References

  • Akuzum Y, Deveci O. The Hadamard-type k-step Fibonacci sequences in groups. Communications in Algebra. 48(7), 2020, 2844−2856.
  • Aydin H, Dikici R. General Fibonacci sequences in finite groups. Fibonacci Quarterly. 36(3), 1998, 216−221.
  • Campbell CM, Doostie H, Robertson EF. Fibonacci length of generating pairs in groups. In: Bergum, G. E., ed. Applications of Fibonacci Numbers. Vol. 3. Springer, Dordrecht: Kluwer Academic Publishers, 1990, pp. 27−35.
  • Deveci O, Karaduman E. On the Padovan p-numbers. Hacettepe Journal of Mathematics and Statistics. 46(4), 2017, 579−592.
  • Deveci O, Akuzum Y, Karaduman E. The Pell-Padovan p-Sequences and Its Applications. Utilitas Mathematica. 98, 2015, 327−347.
  • Deveci O, Akuzum Y. The Cyclic Groups and The Semigroups via MacWilliams and Chebyshev Matrices. Journal of Mathematics Research. 6(2), 2014, 55−58.
  • Deveci O, Shannon AG. The complex-type k-Fibonacci sequences and their applications. Communications in Algebra. 49(3), 2021, 1352−1367.
  • Doostie H, Hashemi M. Fibonacci lengths involving the Wall number K(n). Journal of Applied Mathematics and Computing. 20(1-2), 2006, 171−180.
  • Erdag O, Halıcı S, Deveci O. The Complex-Type Padovan-p Sequences. is submitted.
  • Falcon S, Plaza A. k-Fibonacci sequences modulo m. Chaos, Solitons and Fractals. 41(1), 2009, 497−504.
  • Karaduman E, Aydın H. k-nacci sequences in some special groups of finite order. Mathematical and Computer Modelling. 50(1-2), 2009, 53−58.
  • Knox SW. Fibonacci sequences in finite groups, Fibonacci Quarterly. 30(2), 1992, 116−120.
  • Lu K, Wang J. k-step Fibonacci sequence modulo m. Utilitas Mathematica. 71, 2006, 169−177.
  • Ozkan E, Aydin H, Dikici R. 3-step Fibonacci series modulo m. Applied Mathematics and Computation. 143(1), 2003, 165−172.
  • Wall DD. Fibonacci series modulo m, American Mathematical Monthly. 67(6), 1960, 525−532.
  • Wilcox HJ. Fibonacci sequences of period n in Groups. Fibonacci Quarterly. 24(4), 1986, 356−361.
There are 16 citations in total.

Details

Primary Language English
Journal Section Volume VI Issue III
Authors

Ömür Deveci 0000-0001-5870-5298

Özgür Erdağ 0000-0001-8071-6794

Publication Date December 30, 2021
Published in Issue Year 2021 Volume: 6 Issue: 3

Cite

APA Deveci, Ö., & Erdağ, Ö. (2021). The Period and Rank of the Complex-type Padovan-p Numbers Modulo m. Turkish Journal of Science, 6(3), 156-161.
AMA Deveci Ö, Erdağ Ö. The Period and Rank of the Complex-type Padovan-p Numbers Modulo m. TJOS. December 2021;6(3):156-161.
Chicago Deveci, Ömür, and Özgür Erdağ. “The Period and Rank of the Complex-Type Padovan-P Numbers Modulo M”. Turkish Journal of Science 6, no. 3 (December 2021): 156-61.
EndNote Deveci Ö, Erdağ Ö (December 1, 2021) The Period and Rank of the Complex-type Padovan-p Numbers Modulo m. Turkish Journal of Science 6 3 156–161.
IEEE Ö. Deveci and Ö. Erdağ, “The Period and Rank of the Complex-type Padovan-p Numbers Modulo m”, TJOS, vol. 6, no. 3, pp. 156–161, 2021.
ISNAD Deveci, Ömür - Erdağ, Özgür. “The Period and Rank of the Complex-Type Padovan-P Numbers Modulo M”. Turkish Journal of Science 6/3 (December 2021), 156-161.
JAMA Deveci Ö, Erdağ Ö. The Period and Rank of the Complex-type Padovan-p Numbers Modulo m. TJOS. 2021;6:156–161.
MLA Deveci, Ömür and Özgür Erdağ. “The Period and Rank of the Complex-Type Padovan-P Numbers Modulo M”. Turkish Journal of Science, vol. 6, no. 3, 2021, pp. 156-61.
Vancouver Deveci Ö, Erdağ Ö. The Period and Rank of the Complex-type Padovan-p Numbers Modulo m. TJOS. 2021;6(3):156-61.