A purely exponential Diophantine equation in three unknowns

Miyazaki, Takafumi; Sudo, Masaki; Terai, Nobuhiro

doi:10.1007/s10998-021-00405-x

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2022

2024

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Cited by 4 publications

(2 citation statements)

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“…G. Janaki and C. Saranya (4) established that positive integer solutions exist to the exponential problem using Jarasandha numbers employing the Catalan conjecture. Several exponential Diophantine equations are solved by many authors in (5)(6)(7)(8)(9)(10)(11)(12) .…”

Section: Introductionmentioning

confidence: 99%

(Exponential Diophantine Equation n2􀀀1 )u +n2v = w2;n = 2;3;4;5

Janaki,

Shankari

2024

IJST

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Section: Introductionmentioning

confidence: 99%

(Exponential Diophantine Equation n2􀀀1 )u +n2v = w2;n = 2;3;4;5

Janaki,

Shankari

2024

IJST

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“…, where or p is a prime congruent to 1 (mod 8), does not have a solution in non-negative integers [24]. A heuristic list of the positive integer solutions x, y , and z of the Diophantine equation ( ) is described by Miyazaki et al [25]. All the explicit solutions of the Diophantine equation are also found using lower bounds for linear forms in logarithms and properties of continued fractions [26].…”

Section: Introductionmentioning

confidence: 99%

Does the Solution to the Non-linear Diophantine Equation 3x+35y=Z2 Exist?

Biswas¹

2022

J. Sci. Res.

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This paper investigates the solutions (if any) of the Diophantine equation 3x + 35y = Z2, where , x, y, and z are whole numbers. Diophantine equations are drawing the attention of researchers in diversified fields over the years. These are equations that have more unknowns than a number of equations. Diophantine equations are found in cryptography, chemistry, trigonometry, astronomy, and abstract algebra. The absence of any generalized method by which each Diophantine equation can be solved is a challenge for researchers. In the present communication, it is found with the help of congruence theory and Catalan’s conjecture that the Diophantine equation 3x + 35y = Z2 has only two solutions of (x, y, z) as (1, 0, 2) and (0, 1, 6) in non-negative integers.

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