Matrices, Recurrent Sequences and Arithmetic

Umberto Cerruti and Francesco Vaccarino

A chapter in Applications of Fibonacci Numbers, 1996, pp 53-62 from Springer

Abstract: Abstract The aim of this paper is to give a method, based on linear algebra techniques, thanks to which, the authors are also able to generalize older results on recurrent sequences to commutative rings with identity, often giving proofs essentially different to the ones previously given. In paragraph 2, is also proved a theorem which tells us, in a precise manner, how an impulse response sequence determines all the others having the same characteristic polynomial. In the third paragraph, among the other results, two theorems are proved: the former allow to prove (in an immediate way) a result on decimated sequences, which was given in [6], the latter gives rise to two really surprising arithmetical applications, which are explained in the fourth paragraph. The results here obtained are all proved in an elementary way, notwithstanding their generality.

Date: 1996
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DOI: 10.1007/978-94-009-0223-7_5

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