Let c be a square-free positive integer and pa prime satisfying p\not ∣ cp∤ c. Let h (-c) h (-c)
denote the class number of the imaginary quadratic field Q (-c) Q (-c). In this paper, we …

On certain prime numbers in Lucas sequences 1 Introduction Page 1 On certain prime numbers
in Lucas sequences Ali S. Athab 1 Hayder R. Hashim Faculty of Computer Science and …

Abstract Generalized Fibonacci and Lucas sequences ($ U_n $) and ($ V_n $) are defined
by the recurrence relations $ U_ {n+ 1}= PU_n+ QU_ {n-1} $ and $ V_ {n+ 1}= PV_n+ QV_ {n …

Let $ P\geq 3$ be an integer. Let $(V_ {n}) $ denote generalized Lucas sequence defined by
$ V_ {0}= 2$, $ V_ {1}= P $, and $ V_ {n+ 1}= PV_ {n}-V_ {n-1} $ for $ n\geq 1$. In this study …

We investigate the solvability of the Diophantine equation in the title, where d> 1 d> 1 is a
square-free integer, p, q are distinct odd primes and x, y, a, b are unknown positive integers …

Let P be a nonzero integer and let (U_ n)(U n) and (V_ n)(V n) denote Lucas sequences of
first and second kind defined by U_ 0= 0, U_ 1= 1; V_ 0= 2, V_ 1= P; U 0= 0, U 1= 1; V 0= 2 …

In this thesis we investigate selected properties of base-b expansions of terms of interesting
number sequences, including factorials, linear recurrence sequences, polynomials and p …

This dissertation deals with some types of Diophantine equations related to linear
recurrence sequences. In fact, it consists of three chapters. In Section 1.1, we introduce a …

Abstract Let P ≥ 3 P≥ 3 be an integer and let (U_ n)(U n) and (V_ n)(V n) denote
generalized Fibonacci and Lucas sequences defined by U_ 0= 0, U_ 1= 1 U 0= 0, U 1= 1; …

In 1989, Ming Luo\cite {L2} showed that the Fibonacci number $ U_n $ is Triangular if and
only if $ n=\pm1, 2, 4, 8, 10$. For this, he established a Jacobi Symbol Criterion. Moreover …