Results 11 to 20 of about 2,595 (231)
The Diophantine Equation 8x+py=z2 [PDF]
The Scientific World Journal, 2015 Let p be a fixed odd prime. Using certain results of exponential Diophantine equations, we prove that (i) if p≡±3(mod 8), then the equation 8x+py=z2 has no positive integer solutions (x,y,z); (ii) if p≡7(mod 8), then the equation has only the solutions
Lan Qi, Xiaoxue Li
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The Exponential Diophantine Equation 2x+by=cz [PDF]
The Scientific World Journal, 2014 Let b and c be fixed coprime odd positive integers with min{b,c}>1. In this paper, a classification of all positive integer solutions (x,y,z) of the equation 2x+by=cz is given. Further, by an elementary approach, we prove that if c=b+2, then the equation
Yahui Yu, Xiaoxue Li
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The Diophantine equation x2+2k=yn, II [PDF]
International Journal of Mathematics and Mathematical Sciences, 1999 New results regarding the full solution of the diophantine equation x2+2k=yn in positive integers are obtained. These support a previous conjecture, without providing a complete proof.
J. H. E. Cohn
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The diophantine equation r2+r(x+y)=kxy [PDF]
International Journal of Mathematics and Mathematical Sciences, 1985 The Diophantine equation of the title is solved in integers.
W. R. Utz
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Diophantine equations involving factorials [PDF]
Mathematica Bohemica, 2017 We study the Diophantine equations $(k!)^n -k^n = (n!)^k-n^k$ and $(k!)^n +k^n = (n!)^k +n^k,$ where $k$ and $n$ are positive integers. We show that the first one holds if and only if $k=n$ or $(k,n)=(1,2),(2,1)$ and that the second one holds if and only
Horst Alzer, Florian Luca
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On a Diophantine Equation of Stroeker [PDF]
Bulletin of the Belgian Mathematical Society - Simon Stevin, 2010 The authors prove that there are infinitely many positive integers \(N\) such that the Diophantine equation \((x^2+y)(x+y^2)=N(x-y)^3\) has no nontrivial integer solution \((x,y)\).
Luca, Florian +2 more
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The Diophantine equation ax2+2bxy−4ay2=±1 [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 We discuss, with the aid of arithmetical properties of the ring of the Gaussian integers, the solvability of the Diophantine equation ax2+2bxy−4ay2=±1, where a and b are nonnegative integers.
Lionel Bapoungué
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On the Diophantine equation $(2^x-1)(p^y-1)=2z^2$ [PDF]
, 2021 summary:Let $p$ be an odd prime. By using the elementary methods we prove that: (1) if $2\nmid x$, $p\equiv \pm 3\pmod 8,$ the Diophantine equation $(2^{x}-1)(p^{y}-1)=2z^{2}$ has no positive integer solution except when $p=3$ or $p$ is of the form $p ...
Tong, Ruizhou
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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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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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