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On F(p, n)-Fibonacci bicomplex numbers

Liana M., Szynal-Liana A., Włoch I.

Scientific Issues of Jan Długosz University in Częstochowa. Mathematics

2018

Vol. 23

35--44

In this paper we introduce F(p, n)-Fibonacci bicomplex numbers and L(p, n)-Lucas bicomplex numbers as a special type of bicomplex numbers. We give some their properties and describe relations between them.

Prace Andrzeja Rotkiewicza z teorii liczb

Schinzel A.

Wiadomości Matematyczne

2017

T. 53, nr 2

291--301

W artykule omawiane są prace Andrzeja Rotkiewicza z teorii liczb dotyczące liczb pseudopierwszych, liczb Lucasa i Lehmera oraz równań diofantycznych.

Binomials transformation formulae of scaled Lucas numbers

Wituła R.

Demonstratio Mathematica

2013

Vol. 46, nr 1

15--27

The current paper represents a suplement for papers [7] and [8]. Many of the new summation formulae connecting Lucas numbers with binomials are presented here. All these relations are obtained by using definition and simple properties of the so called δ-Lucas numbers.

Sums of products of generalized Fibonacci and Lucas numbers

Cerin Z.

Demonstratio Mathematica

2009

Vol. 42, nr 2

247-258

In this paper we obtain explicit formulae for sums of products of a fixed number of consecutive generalized Fibonacci and Lucas numbers. These formulae are related to the recent work of Belbachir and Bencherif. We eliminate all restrictions about the initial values and the form of the recurrence relation. In fact, we consider six different groups of three sums that include alternating sums and sums in which terms are multiplied by binomial coefficients and by natural numbers. The proofs are direct and use the formula for the sum of the geometric series.