Correction to: X-coordinates of Pell equations as sums of two Tribonacci numbers

Bravo, Eric F.; Gómez, Carlos A.; Luca, Florian

doi:10.1007/s10998-019-00305-1

Cited by 4 publications

(9 citation statements)

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“…In this paper, we study the same problem considered by E. F. Bravo et al [3,4] but with Padovan numbers instead of Tribonacci numbers. We also extend the results from the Pell equation (1) to the Pell equation (2).…”

Section: Resultsmentioning

confidence: 99%

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On the x-coordinates of Pell equations that are sums of two Padovan numbers

Ddamulira

2021

Bol. Soc. Mat. Mex.

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Let $$ (P_{n})_{n\ge 0} $$ ( 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 for all $$ n\ge 0 $$ n ≥ 0 . In this paper, we find all positive square-free integers d such that the Pell equations $$ x^2-dy^2 = N $$ x 2 - d y 2 = N with $$ N\in \{\pm 1, \pm 4\} $$ N ∈ { ± 1 , ± 4 } , have at least two positive integer solutions (x, y) and $$(x^{\prime }, y^{\prime })$$ ( x ′ , y ′ ) such that both x and $$x^{\prime }$$ x ′ are sums of two Padovan numbers.

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Section: Resultsmentioning

confidence: 99%

“…(5) has the two solutions ðk; nÞ ¼ fð1; 3Þ; ð2; 5Þg. Inspired by the main result of Luca et al [17], E. F. Bravo et al [3,4] studied the Diophantine equation…”

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confidence: 99%

On the x-coordinates of Pell equations that are sums of two Padovan numbers

Ddamulira

2021

Bol. Soc. Mat. Mex.

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“…This is sequence A000931 on the On-Line Encyclopedia of Integer Sequences (OEIS) [21]. The first few terms of this sequence are 3,4,5,7,9,12,16,21,28,37,49,65,86,114,151, . .…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we let U := {P n P m : n ≥ m ≥ 0} be the sequence of products of two Padovan numbers. The first few members of U are U = {0, 1, 2, 3,4,5,6,7,8,9,10,12,14,15,16,18,20,21,24,25, 27, 28, 32, 35, . .…”

Section: Introductionmentioning

confidence: 99%