On linear difference equations over rings and modules.
On linear recurrence relations satisfied by Pisot sequences
On linear recurrence relations satisfied by Pisot sequences - Addenda and errata
On pairings of the first 2n natural numbers
On polynomials with flat squares
On prime-detecting sequences from Apéry's recurrence formulae for and .
On reciprocal sums of terms of linear recurrences
On recurrences of Fahr and Ringel arising in graph theory.
On recurrent mod p sequences.
On Rowland's sequence.
On some arithmetical properties of Lucas and Lehmer numbers
On some combinatorial properties of generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions
We study generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions. We present some properties of these quaternions and the relations between the generalized commutative Jacobsthal quaternions and generalized commutative Jacobsthal-Lucas quaternions.
On some non-holonomic sequences.
On some properties of bivariate Fibonacci and Lucas polynomials.
On square classes in generalized Fibonacci sequences
Let P and Q be nonzero integers. The generalized Fibonacci and Lucas sequences are defined respectively as follows: U₀ = 0, U₁ = 1, V₀ = 2, V₁ = P and , for n ≥ 1. In this paper, when w ∈ 1,2,3,6, for all odd relatively prime values of P and Q such that P ≥ 1 and P² + 4Q > 0, we determine all n and m satisfying the equation Uₙ = wUₘx². In particular, when k|P and k > 1, we solve the equations Uₙ = kx² and Uₙ = 2kx². As a result, we determine all n such that Uₙ = 6x².
On sums of powers of terms in a linear recurrence.
On sums of -units and linear recurrences
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 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