In this paper, by using linear forms in logarithms and the Baker–Davenport reduction procedure we prove that there are no even perfect numbers appearing in generalized Pell sequences. We also deduce some interesting results involving generalized Pell numbers, which we believe are of independent interest. This paper continues a previous work that searched for perfect numbers in the classical Pell sequence.

中文翻译：

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即使是广义佩尔序列中的完美数

在本文中，通过使用对数中的线性形式和 Baker-Davenport 约简过程，我们证明了在广义 Pell 序列中不存在偶数完全数。我们还推导出了一些涉及广义佩尔数的有趣结果，我们认为这些结果具有独立意义。本文延续了之前在经典佩尔序列中搜索完美数的工作。