VALUES OF BERNOULLI AND EULER POLYNOMIALS AT RATIONAL POINTS

期刊： FIBONACCI QUARTERLY, 2021; 59 (1)

A problem proposed by E. Lehmer about Bernoulli polynomials is solved, using a classic theorem of D. H. Lehmer. A similar result is obtained for Euler......

DIVISIBILITY PROPERTIES OF FACTORS OF THE DISCRIMINANT OF GENERALIZED FIBONACCI NUMBERS

期刊： FIBONACCI QUARTERLY, 2021; 59 (1)

We study some divisibility properties related to the factors of the discriminant of the characteristic polynomial of generalized Fibonacci numbers (G(......

EXTENDING ZECKENDORF'S THEOREM TO A NON-CONSTANT RECURRENCE AND THE ZECKENDORF GAME ON THIS NON-CONSTANT RECURRENCE RELATION

期刊： FIBONACCI QUARTERLY, 2020; 58 (5)

Zeckendorf's Theorem states that every positive integer can be uniquely represented as a sum of non-adjacent Fibonacci numbers, indexed from 1, 2, 3, ......

CONVOLUTIONS OF GENERALIZED STIRLING NUMBERS AND DEGENERATE BERNOULLI POLYNOMIALS

期刊： FIBONACCI QUARTERLY, 2020; 58 (4)

We present a general convolution formula involving the generalized Stirling numbers of Hsu and Shiue and the degenerate Bernoulli polynomials of Carli......

GAUSSIAN BEHAVIOR IN ZECKENDORF DECOMPOSITIONS FROM LATTICES

期刊： FIBONACCI QUARTERLY, 2019; 57 (3)

Zeckendorf's Theorem states that any positive integer can be written uniquely as a sum of nonadjacent Fibonacci numbers. We consider higher-dimensiona......

THE PARAMETRIC PASCAL RHOMBUS

期刊： FIBONACCI QUARTERLY, 2019; 57 (4)

In this note, we first show a connection between the complete central coefficients of the Pascal rhombus and the row sums of the left-bounded rhombus.......