On sums of powers of terms in a linear recurrence.
On sums of powers of the positive integers
The pairs (k,m) are studied such that for every positive integer n we have .
On sums of -units and linear recurrences
On sums of sequences of integers, I
On sums of squares of Pell-Lucas numbers.
On sum-sets and product-sets of complex numbers
We give a simple argument that for any finite set of complex numbers , the size of the the sum-set, , or the product-set, , is always large.
On sumsets and spectral gaps
On symmetric and antisymmetric balanced binary sequences.
On systems of composite Lehmer numbers with prime indices
On terms of linear recurrence sequences with only one distinct block of digits
In 2000, Florian Luca proved that F₁₀ = 55 and L₅ = 11 are the largest numbers with only one distinct digit in the Fibonacci and Lucas sequences, respectively. In this paper, we find terms of a linear recurrence sequence with only one block of digits in its expansion in base g ≥ 2. As an application, we generalize Luca's result by finding the Fibonacci and Lucas numbers with only one distinct block of digits of length up to 10 in its decimal expansion.
On ternary inclusion-exclusion polynomials.
On Ternary Integral Recurrences
We prove that if a,b,c,d,e,m are integers, m > 0 and (m,ac) = 1, then there exist infinitely many positive integers n such that m|(an+b)cⁿ - deⁿ. Hence we derive a similar conclusion for ternary integral recurrences.
On the (3N+1)-conjecture
On the Addition of Residue Classes mod p.
On the additive complements of the primes and sets of similar growth
On the additive completion of primes
On the apostol-bernoulli polynomials
In the present paper, we obtain two new formulas of the Apostol-Bernoulli polynomials (see On the Lerch Zeta function. Pacific J. Math., 1 (1951), 161–167.), using the Gaussian hypergeometric functions and Hurwitz Zeta functions respectively, and give certain special cases and applications.
On the appearance of primes in linear recursive sequences.
On the Arithmetic of Special Values of L Functions.
On the arrowhead-Fibonacci numbers
In this paper, we define the arrowhead-Fibonacci numbers by using the arrowhead matrix of the characteristic polynomial of the k-step Fibonacci sequence and then we give some of their properties. Also, we study the arrowhead-Fibonacci sequence modulo m and we obtain the cyclic groups from the generating matrix of the arrowhead-Fibonacci numbers when read modulo m. Then we derive the relationships between the orders of the cyclic groups obtained and the periods of the arrowhead-Fibonacci sequence...