A GENERALISATION OF THE DIOPHANTINE EQUATION x^2+8∙7^b=y^2r

Sapar, Siti Hasana; Yow, Kai Siong

doi:10.22452/mjs.vol40no2.3

Cited by 2 publications

(1 citation statement)

References 8 publications

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“…When 𝑛 is even, Yow (2011) found that there exist infinitely many solutions to the equation. The generalisations for the cases when 𝑎 = 2 and 𝑎 = 3 can be found in Yow et al (2013) and Sapar et al (2021), respectively.…”

Section: Introductionmentioning

confidence: 91%

Solutions to the Diophantine Equation x²+16⋅7ᵇ=y²ʳ

Yow

Sapar

Low

2022

Mal. J. Fund. Appl. Sci.

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We present a method of determining integral solutions to the equation x^2 + 16.7^b = y^2r, where x,y,b,r \in Z^+. We observe that the results can be classified into several categories. Under each category, a general formula is obtained by using the method of geometric progression. 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 respective values of x and y^r. We also highlight two special cases where different formulae are needed to represent their integral solutions.

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Section: Introductionmentioning

confidence: 91%

Solutions to the Diophantine Equation x²+16⋅7ᵇ=y²ʳ

Yow

Sapar

Low

2022

Mal. J. Fund. Appl. Sci.

Self Cite

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On properties and operations of complex neutrosophic soft groups

Rahoumah,

Yow,

Nik Long

et al. 2024

J Inequal Appl

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Complex neutrosophic soft groups represent a significant advancement in handling uncertainty by integrating the concepts of fuzzy logic, soft sets, and neutrosophic logic. These groups generalize complex fuzzy soft groups and introduce an additional dimension through neutrosophic membership functions, namely truth, indeterminacy, and falsity. This creates a richer framework for dealing with uncertainty and ambiguity, making it well-suited for managing complex data structures in real-world applications. We explore some important definitions and theoretical frameworks surrounding complex neutrosophic soft groups, highlighting the unique aspect of neutrosophic membership functions. Additionally, we present an overview of neutrosophic soft groups, exploring some of their key operations and fundamental properties. We then examine the basics of homogeneous complex neutrosophic soft sets and their roles in establishing complex neutrosophic soft groups.

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A GENERALISATION OF THE DIOPHANTINE EQUATION x^2+8∙7^b=y^2r

Cited by 2 publications

References 8 publications

Solutions to the Diophantine Equation x²+16⋅7ᵇ=y²ʳ

Solutions to the Diophantine Equation x²+16⋅7ᵇ=y²ʳ

On properties and operations of complex neutrosophic soft groups

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