Perfect squares in the sum and difference of balancing-like numbers
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Published:2022-05-12
Issue:2
Volume:28
Page:286-301
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ISSN:1310-5132
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Container-title:Notes on Number Theory and Discrete Mathematics
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language:
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Short-container-title:NNTDM
Author:
Sahukar M. K., ,Şiar Zafer,Keskin Refik,Panda G. K., , ,
Abstract
In this study, we deal with the existence of perfect powers which are sum and difference of two balancing numbers. Moreover, as a generalization we explore the perfect squares which are sum and difference of two balancing-like numbers, where balancing-like sequence is defined recursively as $G_{n+1}=AG_n-G_{n-1}$ with initial terms $G_0=0,G_1=1$ for $A \geq 3$.
Publisher
Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences)