Mathematics, 2021 Consider the Diophantine equation yn=x+x(x+1)+⋯+x(x+1)⋯(x+k), where x, y, n, and k are integers. In 2016, a research article, entitled – ’power values of sums of products of consecutive integers’, primarily proved the inequality n= 19,736 to obtain all ...
S. Subburam +6 more
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The mathematical analysis of Linear Diophantine equations with two and three variables and Its Applications [PDF]
The Egyptian International Journal of Engineering Sciences and Technology, 2023 Linear Diophantine equation are introduced to determine and search for integral solutions according to the associated variables. In this paper, the mathematical techniques are approached to solve Linear Diophantine equation with two, three unknowns and ...
Rania Amer
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On the solution of the exponential Diophantine equation 2x+m2y=z2, for any positive integer m [PDF]
Journal of Hyperstructures, 2023 It is well known that the exponential Diophantine equation 2x+ 1=z2 has the unique solution x=3 and z=3 innon-negative integers, which is closely related to the Catlan's conjecture.
Mridul Dutta, Padma Bhushan Borah
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On some Diophantine equations [PDF]
Miskolc Mathematical Notes, 2021 In this paper we deal with some Diophantine equations and present infinitely many positive integer solutions for each one of them.
Bujačić Babić, Sanda, Nabardi, Kamran
openaire +5 more sources
The integer solutions of the cubic Diophantine equation x3±33=pqy2
Xi'an Gongcheng Daxue xuebao, 2021 The solvability of a class of cubic Diophantine equations is studied by using properties of congruence, Legendre symbol and the methods of elementary number theory.
Heng LI, Hai YANG, Yongliang LUO
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Neutrosophic Linear Diophantine Equations with Two Variables [PDF]
Neutrosophic Sets and Systems, 2020 This paper studies for the first time the neutrosophic linear Diophantine equations with two variables in the neutrosophic ring of integers, and refined neutrosophic ring of integers.
Hasan Sankari, Mohammad Abobala
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Gaussian Integer Solutions of the Diophantine Equation x^4+y^4=z^3 for x≠ y
مجلة بغداد للعلوم, 2023 The investigation of determining solutions for the Diophantine equation over the Gaussian integer ring for the specific case of is discussed.
Shahrina Ismail +3 more
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From Diophantian Equations to Matrix Equations (III) - Other Diophantian Quadratic Equations and Diophantian Equations of Higher Degree [PDF]
Educaţia 21, 2023 In this paper, we propose to continue the steps started in the first two papers with the same generic title and symbolically denoted by (I) and (II), namely, the presentation of ways of achieving a systemic vision on a certain mathematical notional ...
Teodor Dumitru Vălcan
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RETRACTED: On the Nature of Some Euler’s Double Equations Equivalent to Fermat’s Last Theorem
Mathematics, 2022 In this work, I provide a new rephrasing of Fermat’s Last Theorem, based on an earlier work by Euler on the ternary quadratic forms. Effectively, Fermat’s Last Theorem can be derived from an appropriate use of the concordant forms of Euler and from an ...
Andrea Ossicini
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On Phi-Euler's Function in Refined Neutrosophic Number Theory and The Solutions of Fermat's Diophantine Equation [PDF]
Neutrosophic Sets and Systems, 2023 The objective of this paper is to answer the open problem proposed about the validity of phi-Euler’s theorem in the refined neutrosophic ring of integers 𝑍(𝐼1,𝐼2) .
Josef Al Jumayel +2 more
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