Results 151 to 160 of about 312 (174)
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Exponential diophantine equations
Let \(\mathbb G\) be a commutative algebraic group over \(\mathbb C\), not containing any algebraic subgroup isomorphic to the additive group \(\mathbb G_ a\). Let \(\Gamma\) be a subgroup of \(\mathbb G(\mathbb C)\) of finite rank, that is, there is a finitely generated subgroup \(\Gamma'\) of \(\Gamma\) such that all elements of \(\Gamma/\Gamma ...openaire +4 more sources
Classification of Quantifier Prefixes Over Exponential Diophantine Equations
Mathematical Logic Quarterly, 1986After Matijasevič had solved the \(10^{th}\) problem of Hilbert in 1970, it was natural to consider other similar problems. The \(10^{th}\) problem of Hilbert can be viewed as the problem of classification of the quantifier prefix \(\exists\exists\ldots\exists\) over diophantine equations (polynomial equations).
James P. Jones +2 more
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Some conjectures in the theory of exponential Diophantine equations
Publicationes Mathematicae Debrecen, 2000The author formulates a conjecture which implies Pillai's conjecture and a theorem of \textit{A. Schinzel} and \textit{R. Tijdeman} [Acta Arith. 31, 199-264 (1976; Zbl 0339.10018)] that for a polynomial with integer coefficients and at least two distinct roots, there are only finitely many perfect powers in its values at integral points.
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ON EXPONENTIAL DIOPHANTINE EQUATIONS CONTAINING THE EULER QUOTIENT
Bulletin of the Australian Mathematical Society, 2014AbstractLet $a$ and $m$ be relatively prime positive integers with $a>1$ and $m>2$. Let ${\it\phi}(m)$ be Euler’s totient function. The quotient $E_{m}(a)=(a^{{\it\phi}(m)}-1)/m$ is called the Euler quotient of $m$ with base $a$. By Euler’s theorem, $E_{m}(a)$ is an integer.
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Exponential Diophantine equations over function fields
Publicationes Mathematicae Debrecen, 1992Let \(k\) be an algebraically closed field of characteristic zero and let \(k(t)\) be the field of rational functions over \(k\). Further, let \(\mathbb{K}\) be a finite extension of \(k(t)\). For given non-zero elements \(f_ 1,\ldots,f_ n,g\) of \(\mathbb{K}[X_ 1,\ldots,X_ n]\) \((n\geq 2)\), consider the equation \[ \sum^ n_{i=1}f_ i({\mathbf x ...
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Solutions for a Class of the Exponential Diophantine Equation
Advanced Materials Research, 2013We studied the Diophantine equation x2+4n=y11. By using the elementary method and algebraic number theory, we obtain the following conclusions: (i) Let x be an odd number, one necessary condition which the equation has integer solutions is that 210n-1/11 contains some square factors.
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On the Exponential Diophantine Equation $$(m^2+m+1)^x+m^y=(m+1)^z $$
Mediterranean Journal of Mathematics, 2020Murat Alan
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On the exponential Diophantine equation Pm2
This study investigates numbers that are powers of two and can be expressed as the sum of the squares of any two Pell numbers. We apply Baker's theory of linear forms in logarithms of algebraic numbers, along with a variation of the Baker-Davenport reduction method, to solve the Diophantine equation P-m(2) + P-n(2) = 2a, where m,n, and a are non ...Emin, Ahmet, Ates, Firat
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