在两个Padovan数和的Pell方程的x坐标上。

IF 0.9 Q2 MATHEMATICS BOLETIN DE LA SOCIEDAD MATEMATICA MEXICANA Pub Date : 2021-01-01 Epub Date: 2021-02-23 DOI:10.1007/s40590-021-00312-8

Mahadi Ddamulira

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引用次数: 1

摘要

让P (n) n≥0被P Padovan之序列数字:0 = 0,P = P = 2 = 1, n和P P P + 3 = n + 1 + n”为所有n≥0。在这篇文章里,我们找到所有积极square-free integers d这样的那个《佩尔equations x 2 - d y = N与N∈{±1±4),有至少两个阳性整数解(x, y)和(x, y’)如此那两者x和x '是概括的两个Padovan数字。

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

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 positive square-free integers d such that the Pell equations $x^{2} - d y^{2} = N$ with $N \in {\pm 1, \pm 4}$ , have at least two positive integer solutions (x, y) and $(x^{'}, y^{'})$ such that both x and $x^{'}$ are sums of two Padovan numbers.