Results 151 to 160 of about 92,931 (194)

On The Exponential Diophantine Equation $p^{2m} + {(6r+1)}^n = z^{2}$

Applied mathematics and computational intelligence
A polynomial equation with two or more unknowns for which the integer solutions are sought out is called a Diophantine equation. When exponents are introduced into the equation, a simple linear Diophantine equation transforms into a more complex ...
Nuralia Amira, Mohammad Ikhram, S. H. Sapar, K. S. Yow   +3 more
semanticscholar   +1 more source

On the Exponential Diophantine Equation x2 + p = 2n for Primes p ≡ 7(mod8)

International Journal of Global Sustainable Research
We revisit the Ramanujan–Nagell type exponential Diophantine equation x2+p=2n,  x, n ∈ Z ≥ 1,  p an odd prime,  with emphasis on the congruence class p ≡ 7(mod8).
Amit Kumar
semanticscholar   +1 more source

On the Exponential Diophantine Equation 11^x-13^y=z^3.

International Journal of Mathematical and Computer Sciences
We prove that the exponential Diophantine equation 11^x-13^y=z^3 has the unique non-negative integer solution (x, y, z) = (0, 0, 0). The result is obtained by analyzing the equation under various moduli and utilizing the properties of the order of ...
P. Ardsalee
semanticscholar   +1 more source

On Matrix Elliptic Curves and Matrix Solutions of the Exponential Diophantine Equation (X^{24}-I_{24})(Y^{24}-I_{24})=Z^{2}

Japan Journal of Research
We show that the structures of the matrix solutions of the matrix elliptic curves 2 3 6 EY X I : , α = +× ∈ α α  allow the construction of the matrix solutions of the equations 4 24 6 24 24 2 24 24 XY ZX IY I Z += − −= ,( )( ) .
J. M. Mouanda, Djagwa Dehainsala, Kinvi Kangni   +2 more
semanticscholar   +1 more source

A note on ternary purely exponential diophantine equations

Acta Arithmetica, 2015
Summary: Let \(a,b,c\) be fixed coprime positive integers with \(\min\{a,b,c\}>1\), and let \(m=\max \{a,b,c\}\). Using the Gel'fond-Baker method, we prove that all positive integer solutions \((x,y,z)\) of the equation \(a^x+b^y=c^z\) satisfy \(\max \{x,y,z\}1\).
Hu, Yongzhong, Le, Maohua
openaire   +1 more source

Exponential Diophantine Equations

2019
This paper is a very gentle introduction to solving exponential Diophantine equations using the technology of linear forms in logarithms of algebraic numbers.
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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 ...
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Classification of Quantifier Prefixes Over Exponential Diophantine Equations

Mathematical Logic Quarterly, 1986
After 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, Hilbert Levitz, A. J. Wilkie   +2 more
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Some conjectures in the theory of exponential Diophantine equations

Publicationes Mathematicae Debrecen, 2000
The 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, 2014
AbstractLet $a$ 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.
openaire   +1 more source