The quaternion-Pell sequence
- Publication Type:
- Journal Article
- Communications in Algebra, 2018, 46 (12), pp. 5403 - 5409
- Issue Date:
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© 2018, © 2018 Taylor & Francis. In this paper, we define the quaternion-Pell sequence and derive the generating matrix of the sequence. Then we produce the semigroups using the multiplicative orders of the generating matrix of the quaternion-Pell sequence when read modulo α. We also study the quaternion-Pell sequence modulo α and then we give the relationship among the periods of the quaternion-Pell sequence modulo α and the orders of the semigroups obtained. In addition, we extend the quaternion-Pell sequence to groups. Finally, we obtain the periods of the quaternion-Pell sequences in dihedral groups D 2m as applications of the results obtained.
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