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Title: Solutions to the diophantine equation x² + 16∙7ᵇ = y²ʳ
Authors: Yow, Kai Siong
Sapar, Siti Hasana
Low, Cheng Yaw
Keywords: Engineering::Computer science and engineering
Issue Date: 2022
Source: Yow, K. S., Sapar, S. H. & Low, C. Y. (2022). Solutions to the diophantine equation x² + 16∙7ᵇ = y²ʳ. Malaysian Journal of Fundamental and Applied Sciences, 18(4), 489-496.
Journal: Malaysian Journal of Fundamental and Applied Sciences 
Abstract: We present a method of determining integral solutions to the equation x2 + 16 ∙ 7b = y2r, where x, y, b, r ∈ ℤ+. We observe that the results can be classified into several categories. Under each category, a general formula is obtained using the geometric progression method. We then provide the bound for the number of non-negative integral solutions associated with each b. Lastly, the general formula for each of the categories is obtained and presented to determine the respective values of x and yr. We also highlight two special cases where different formulae are needed to represent their integral solutions.
ISSN: 2289-599X
DOI: 10.11113/mjfas.v18n4.2580
Schools: School of Computer Science and Engineering 
Rights: © 2022 Kai Siong Yow, Siti Hasana Sapar, Cheng Yaw Low. This article is distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use and redistribution provided that the original author and source are credited.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SCSE Journal Articles

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