Contents

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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 (u_{n})_{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 (u_{n})_{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.