On a Diophantine Equation

Tho, Nguyen Xuan

doi:10.1007/s10013-021-00503-w

Cited by 5 publications

(2 citation statements)

References 5 publications

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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].…”

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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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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“…For the representation of positive integers n in the form n = (x [2,11]. For the representation of positive integers n in the form n = x/y + dy/z + z/w + dw/x, where x, y, z, w, d ∈ Z + , see [4,10].…”

Section: Introductionmentioning

confidence: 99%

On a Problem of Richard Guy

Tho

2021

Bull. Aust. Math. Soc.

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In the 1993 Western Number Theory Conference, Richard Guy proposed Problem 93:31, which asks for integers n representable by ${(x+y+z)^3}/{xyz}$ , where $x,\,y,\,z$ are integers, preferably with positive integer solutions. We show that the representation $n={(x+y+z)^3}/{xyz}$ is impossible in positive integers $x,\,y,\,z$ if $n=4^{k}(a^2+b^2)$ , where $k,\,a,\,b\in \mathbb {Z}^{+}$ are such that $k\geq 3$ and $2\nmid a+b$ .

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On Sums of Positive Rationals with Given Products

Tho

2022

Mediterr. J. Math.

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On a Diophantine Equation

Cited by 5 publications

References 5 publications

Does the Solution to the Non-linear Diophantine Equation 3<sup>x</sup>+35<sup>y</sup>=Z<sup>2</sup> Exist?

Does the Solution to the Non-linear Diophantine Equation 3<sup>x</sup>+35<sup>y</sup>=Z<sup>2</sup> Exist?

On a Problem of Richard Guy

On Sums of Positive Rationals with Given Products

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