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Diophantine Equation 4k2−1nx+4kny=4k2+1nz
Journal of MathematicsLet a,b,c be a primitive Pythagorean triple such that a2+b2=c2 with 2b. In 1956, L. Jesmanowicz conjectured that, for any positive integer n, the equation anx+bny=cnz has only the positive solution x,y,z=2,2,2. In 1959, Lu Wenduan claimed that if n=1 and
Nai-juan Deng, Ridi Huang
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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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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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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 the Diophantine Equation Mp^x + (Mq + 1)^y = z^2
, 2021 In this paper, we study and solve the exponential Diophantine equation of the form Mxp + (Mq + 1)y = z2 for Mersenne primes Mp and Mq and non-negative integers x, y, and z.
W. Gayo, Jr., J. Bacani
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A Study of Symbolic 2-Plithogenic Split-Complex Linear Diophantine Equations in Two Variables [PDF]
Neutrosophic Sets and Systems, 2023 The equation 𝐴𝑋 + 𝐵𝑌 = 𝐶 is called symbolic 2-plithogenic linear Diophantine equation with two variables if 𝐴, 𝐵, 𝑋, 𝑌, 𝐶 are symbolic 2-plithogenic split-complex integers.
Rama Asad Nadweh +3 more
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On the Diophantine equation $F_{n}-F_{m}=2^{a}$ [PDF]
Colloquium Mathematicum, 2017 In this paper, we solve Diophantine equation in the tittle in nonnegative integers m,n, and a. In order to prove our result, we use lower bounds for linear forms in logarithms and and a version of the Baker-Davenport reduction method in diophantine ...
Zafer cSiar, R. Keskin
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Matrix Diophantine equations over quadratic rings and their solutions
Karpatsʹkì Matematičnì Publìkacìï, 2020 The method for solving the matrix Diophantine equations over quadratic rings is developed. On the basic of the standard form of matrices over quadratic rings with respect to $(z,k)$-equivalence previously established by the authors, the matrix ...
N.B. Ladzoryshyn +2 more
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, 2020 Let ( F n ) n ≥ 0 be the sequence of the Fibonacci numbers. The order (or rank) of appearance z ( n ) of a positive integer n is defined as the smallest positive integer m such that n divides F m .
Eva Trojovská
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Separable Diophantine Equations [PDF]
Transactions of the American Mathematical Society, 1945 Theoretically, as noted by Skolem [3, p. 21(1), the general problem of algebraic diophantine analysis is reducible to the case in which occur only equations and inequalities of degree not higher than the second. For the extensive class of separable systems defined in ?6, this reduction can be performed effectively, eventuating in the complete integer ...
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