k-Arithmetic Sequences—Theory and Applications

  • Adam Kołacz
Part of the Studies in Computational Intelligence book series (SCI, volume 634)


The notion of an arithmetic progression was extended to embrace the class of polynomials of degree \(k>1\). Some properties of difference sequences are analyzed and their connections with some number-theory problems are studied. In particular, a certain aspects of Fermat’s Last Theorem and the Fibonacci numbers are revisited.


Arithmetic progression Difference sequence Polynomials Fibonacci numbers 

2010 Mathematics Subject Classification



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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Faculty of Mathematics and Information ScienceWarsaw University of TechnologyWarsawPoland

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