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Congruences and identities for some second-order
linear homogeneous recurrent sequences



Hamadoun MAÏGA

DER de Mathématiques et Informatique
Faculté des Sciences et Techniques (FST)
Université des Sciences, des Techniques et
des Technologies de Bamako (USTTB)
BP: E 3206 Bamako, Mali




Mathematics Subject Classification: (2010) Primary: 11S80, 11A07, 11B50, 46S10, 97F60 Secondary: 32P05, 44A10, 44A60
Key words: p-adic measure, moment sequences, exponential generating function, Laplace transform, congruences, identities, Chebyshev polynomials, Fibonacci numbers, Lucas numbers, second-order linear recurrent sequences.

Abstract:


In this paper, we study few properties of the second-order linear homogeneous recurrent sequence (un)n with constant coefficients in a complete valued field extension of the field of p-adic numbers. More precisely, we give the necessary and sufficient condition satisfied by (un)n to be the moment sequence of an appropriate p-adic measure. Furthermore, we establish identities and congruences for Fibonacci numbers, and for some p-adic values of Chebyshev polynomials. Some ones are well known and others, for instance Kummer like congruences, seem to be new.

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