Let $\{P_ {n}\} _ {n\geq 0} $ be the sequence of Padovan numbers defined by $ P_0= 0$, $
P_1= P_2= 1$, and $ P_ {n+ 3}= P_ {n+ 1}+ P_n $ for all $ n\geq 0$. In this paper, we find all …

Let {Ln} n≥ 0 be the sequence of Lucas numbers given by L 0= 2, L 1= 1, and Ln+ 2= Ln+
1+ Ln for all n≥ 0. In this paper, for an integer d≥ 2 that is square-free, we show that there is …

Terms of recurrence sequences in the solution sets of generalized Pell equations Page 1
International Journal of Number Theory Vol. 18, No. 7 (2022) 1605–1612 c© World Scientific …

Let (P n) n≥ 0 be the Pell sequence defined by P 0= 0, P 1= 1 and P n+ 2= 2 P n+ 1+ P n for
n≥ 0 and M k= 2 k-1 be the k-th Mersenne number for k≥ 1. We show that the Diophantine …

Abstract Let (P_ n) _ n ≥ 0 (P n) n≥ 0 be the sequence of Padovan numbers defined by
P_0= 0 P 0= 0, P_1= P_2= 1 P 1= P 2= 1, and P_ n+ 3= P_ n+ 1+ P_n P n+ 3= P n+ 1+ P n …

Abstract Let {X_ ℓ\} _ ℓ ≥ 1 X ℓ ℓ≥ 1 be the sequence of X-coordinates of the positive
integer solutions (X, Y) of the Pell equation X^ 2-dY^ 2= ± 1 X 2-d Y 2=±1 corresponding to a …

Abstract Let {F_ n\} _ n ≥ 0 F nn≥ 0 be the sequence of Fibonacci numbers defined by
F_0= 0 F 0= 0, F_1= 1 F 1= 1 and F_ n+ 2= F_ n+ 1+ F_n F n+ 2= F n+ 1+ F n for all n ≥ 0 …

Correction to: X-coordinates of Pell equations as sums of two Tribonacci numbers |
SpringerLink Skip to main content Advertisement SpringerLink Account Menu Find a journal …

For the Fibonacci sequence the identity F n 2+ F n+ 1 2= F 2 n+ 1 holds for all n≥ 0. Let
X:=(X ℓ) ℓ≥ 1 be the sequence of X-coordinates of the positive integer solutions (X, Y) of the …

Let $(X_ {k}) _ {k\geq 1} $ and $(Y_k) _ {k\geq 1} $ be the sequence of $ X $ and $ Y $-
coordinates of the positive integer solutions $(x, y) $ of the equation $ x^ 2-dy^ 2= t $. In this …