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

Yıl 2021, Cilt: 6 Sayı: 3, 156 - 161, 30.12.2021

Ömür Deveci Özgür Erdağ

Öz

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.

Anahtar Kelimeler

The complex-type Padovan-p sequence, Modulo, Period, Rank.

Kaynakça

• 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.