Results 21 to 30 of about 140 (135)
Nonlinear-Adaptive Mathematical System Identification
Computation, 2017 By reversing paradigms that normally utilize mathematical models as the basis for nonlinear adaptive controllers, this article describes using the controller to serve as a novel computational approach for mathematical system identification.
Timothy Sands
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Zhejiang Daxue xuebao. Lixue ban, 2007 用渐近连分数的性质和Pell方程的解类特点，得到了指数丢番图方程的解（x，y，n）的性质及其较为精确的上界 ...
YANGShi-chun(杨仕椿), HEBo(何波)
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On the Diophantine Equation $(8r^2+1)^x+(r^2-1)^y=(3r)^z$ Regarding Terai's Conjecture
Communications in Advanced Mathematical SciencesThis study establishes that the sole positive integer solution to the exponential Diophantine equation $(8r^2+1)^x+(r^2-1)^y=(3r)^z$ is $(x,y,z)=(1,1,2)$ for all $r>1$.
Murat Alan, Tuba Çokoksen
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Tian’s Conjecture on the Prime Factorization of the Binomial Coefficient
MathematicsTian’s conjecture states that for any fixed distinct prime numbers p1,…,pm, the Diophantine equation n+12=p1α1·p2α2···pmαm in positive integers n,α1,…,αm has at most m solutions.
Zhenbing Zeng +3 more
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On a conjecture on exponential Diophantine equations [PDF]
Acta Arithmetica, 2009 We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\equiv 2 \pmod 4$, $b\equiv 3 \pmod 4$ and $\gcd (a,b,c)=1$. The main result is that if there exists a solution $(x,y,z)=(2,2,r)$ with $r>1$ odd then this is the only solution in integers greater than 1, with the possible exception of finitely many values $(c,r)$. We
Cipu, Mihai, Mignotte, Maurice
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Jeśmanowicz' conjecture on exponential diophantine equations
Functiones et Approximatio Commentarii Mathematici, 2011 Jeśmanowicz' conjecture is the following statement: If \(a\), \(b\), \(c\) are coprime positive integers such that \(a^2+b^2=c^2\) with even \(b\), then the exponential equation \(a^x+b^y=c^z\) has the only solution \((x,y,z)=(2,2,2)\) in positive integers. This paper contains various new results on this conjecture.
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Exponential diophantine equations with four terms
Indagationes Mathematicae, 1992 This article gives some examples how to make exponential diophantine equations more practical. The authors take the large exponential bounds for solutions given by Baker's method to computational available bounds. Let \(p\) and \(q\) be distinct primes less than 200. The main theorems are: (1) Every solution of the equation \(p^ x q^ y\pm p^ z \pm q^ w
Deze, Mo, Tijdeman, R.
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On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. [PDF]
Ramanujan J, 2021 Ddamulira M, Luca F.
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Exponential Diophantine equations [PDF]
Pacific Journal of Mathematics, 1982 Brenner, J. L., Foster, Lorraine L.
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Max–min of polynomials and exponential diophantine equations
Journal of Number Theory, 2010 In the first half of this paper, largely based on earlier work of \textit{R. Dvornicich, U. Zannier}, and the author [Acta Arith. 106, No. 2, 115--121 (2003; Zbl 1020.11018)], it is shown that for \(F \in {\mathbb Z}[x,y]\) one has \(\max_{x \in \mathbb Z \cap [-T,T]} \min_{y \in \mathbb Z} |F(x,y)| = o(T^{1/2})\) as \(T \to \infty\) if and only if ...
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