Results 11 to 20 of about 2,597 (231)
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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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 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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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 $(2^x-1)(p^y-1)=2z^2$ [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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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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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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