Results 151 to 160 of about 446 (186)

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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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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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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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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Diophantine equations involving the Euler totient function

Journal of Number Theory, 2020
Bell Jason
exaly  

Solutions of some quadratic Diophantine equations

Computers and Mathematics With Applications, 2010
Refik Keskin
exaly  

Solving a System of Linear Diophantine Equations with Lower and Upper Bounds on the Variables

Mathematics of Operations Research, 2000
Arjen K Lenstra
exaly