Results 81 to 90 of about 312 (174)
An application of Frey's idea to exponential Diophantine equations
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994 Let \(a\), \(b\), \(c\), \(l\), \(m\), \(n\) be relatively prime positive integers. In this paper it is shown that the equation \(la^ x+ mb^ y= nc^ z\), has a finite number of solutions in positive integers \(x\), \(y\), \(z\), all of which can be effectively determined. The effective procedure is based on: a) \textit{G.
openaire +2 more sources
Unifying Aspects of Generalized Calculus. [PDF]
Entropy (Basel), 2020 Czachor M.
europepmc +1 more source
Uncomputability and complexity of quantum control. [PDF]
Sci Rep, 2020 Bondar DI, Pechen AN.
europepmc +1 more source
Some exponential Diophantine equations III: A new look at the generalized Lebesgue–Nagell equation
Let D be a fixed non-square integer, and let h(4D) denote the class number of binary quadratic primitive forms with discriminant 4D. Let k be a fixed even integer with gcd(D,k)=1.
Soydan, Gökhan, Le, Maohua
core +1 more source
, 2023 In this paper we find non-negative integer solutions for exponential Diophantine equations of the type $p \cdot 3^x+ p^y=z^2,$ where $p$ is a prime number. We prove that such equation has a unique solution $\displaystyle{(x,y,z)=\left(\log_3(p-2), 0, p-1\
Ferreira, G. S. +2 more
core
A Contemporary Design Process for Single-Phase Voltage Source Inverter Control Systems. [PDF]
Sensors (Basel), 2022 Bernacki K, Rymarski Z.
europepmc +1 more source
On some conjectures of exponential Diophantine equations
, 2020 In this paper, we consider the exponential Diophantine equation $a^{x}+b^{y}=c^{z},$ where $a, b, c$ be relatively prime positive integers such that $a^{2}+b^{2}=c^{r}, r\in Z^{+}, 2\mid r$ with $b$ even. That is $$a=\mid Re(m+n\sqrt{-1})^{r}\mid, b=\mid Im(m+n\sqrt{-1})^{r}\mid, c=m^{2}+n^{2},$$ where $m, n$ are positive integers with $m>n, m-n ...
openaire +2 more sources
Topological triple phase transition in non-Hermitian Floquet quasicrystals. [PDF]
Nature, 2022 Weidemann S +3 more
europepmc +1 more source
Singularity of the Spectrum for Smooth Area-Preserving Flows in Genus Two and Translation Surfaces Well Approximated by Cylinders. [PDF]
Commun Math Phys, 2021 Chaika J +3 more
europepmc +1 more source
Translation invariance, exponential sums, and Waring's problem
, 2014 We describe mean value estimates for exponential sums of degree exceeding 2 that approach those conjectured to be best possible. The vehicle for this recent progress is the efficient congruencing method, which iteratively exploits the translation ...
Wooley, Trevor D. +2 more
core