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Local-global principles for recurrence sequences

100%

Schinzel A. , Skałba M.

2019

tom Vol. 67, no. 1

37--40

A proof is given that if a non-degenerate recurrence sequence of the second order over the rationals with separable companion equation contains multiples of infinitely many terms of the Lucas sequence governed by the same recurrence, then it contains zero for an index of a suitable sign.

Cauchy, Ferrers-Jackson and Chebyshev polynomials and identities for the powers of elements of some conjugate recurrence sequences

51%

Wituła R. , Słota D.

tom 4

nr 3

531-546

In this paper some decompositions of Cauchy polynomials, Ferrers-Jackson polynomials and polynomials of the form x 2n + y 2n , n ∈ ℕ, are studied. These decompositions are used to generate the identities for powers of Fibonacci and Lucas numbers as well as for powers of the so called conjugate recurrence sequences. Also, some new identities for Chebyshev polynomials of the first kind are presented here.