Results 131 to 140 of about 1,430,683 (165)

A class of Diophantine equations

Publicationes Mathematicae Debrecen, 1992
A method is given for the resolution of diophantine equations of type \(F(2^ a\cdot 3^ b)=\pm 2^ c\cdot 3^ d\), where \(F(x)\in\mathbb{Z}[x]\) has at least two distinct roots. The method is based on lower bounds for linear forms in logarithms of algebraic numbers and the LLL-lattice basis reduction algorithm.
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Aggregating diophantine equations

Zeitschrift für Operations Research, 1972
Mathews [1897] has given a theorem for aggregating two diophantine equations with positive integer coefficients into a single equation that has the same solution set as its parents over the nonnegative integers. Building on this result,Elmaghraby andWig [1970] show how to shrink the inequality constraints of a bounded variable integer program to a ...
Fred W. Glover, Robert E. D. Woolsey
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Quadratic diophantine equations

Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 1960
Abstract Tartakowsky (1929) proved that a positive definite quadratic form, with integral coefficients, in 5 or more variables represents all but at most finitely many of the positive integers not excluded by congruence considerations.
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Universal diophantine equation

Journal of Symbolic Logic, 1982
In 1961 Martin Davis, Hilary Putnam and Julia Robinson [2] proved that every recursively enumerable set W is exponential diophantine, i.e. can be represented in the formHere P is a polynomial with integer coefficients and the variables range over positive integers.In 1970 Ju. V.
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A Class of Diophantine Equations

The Mathematical Gazette, 1938
The general solution in positive integers of the equation (1) 2 a(x 2 − y 2 ) + l = z 2 where
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Notes on diophantine equations

1953
Verschiedene Bemerkungen und Parameterlösungen zu den Diophantischen Gleichungen \[ x^2+ y^2 + z^2 = 1, \quad A(x^2+ y^2 + z^2) = B(xy + x z + yz), \] und \[ (r^4 + s^4) x^4 - y^4 = z^2 \quad\text{und}\quad (r^4 - s^4) x^4 + y^4 = z^2. \]
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Diophantine Equations and Computation

2009
Unless otherwise stated, we'll work with the natural numbers : $$N = \{0,1,2,3, \dots\}.$$ Consider a Diophantine equation F (a 1 ,a 2 ,...,a n ,x 1 ,x 2 ,...,x m ) = 0 with parameters a 1 ,a 2 ,...,a n and unknowns x 1 ,x 2 ,...,x m For such a given equation, it is usual to ask: For which values of the parameters does the equation have a ...
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Quadratic Diophantine Equations

2004
34.1. We take a nondegenerate quadratic space \((V,\,{\varphi})\) of dimension \(\,n\,\) over a local or global field F in the sense of §21.1.
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A Diophantine Equation

Journal of the London Mathematical Society, 1968
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On the Solutions of the Diophantine Equation p^(x) +(p+4k)^(y)=Z² for Prime Pairs p and $p+4k$

European Journal of Pure and Applied Mathematics, 2021
Jerico B. Bacani
exaly