Perfect squares in the sum and difference of balancing-like numbers
- 12 May 2022
- journal article
- research article
- Published by Prof. Marin Drinov Publishing House of BAS (Bulgarian Academy of Sciences) in Notes on Number Theory and Discrete Mathematics
- Vol. 28 (2), 286-301
- https://doi.org/10.7546/nntdm.2022.28.2.286-301
Abstract
In this study, we deal with the existence of perfect powers which are the sum and difference of two balancing numbers. Moreover, as a generalization we explore the perfect squares which are the 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 >= 3.Keywords
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