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Diophantine Approximations and Diophantine Equations

, 1991
"This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations.
Schmidt, Wolfgang M
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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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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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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
J C Saunders
exaly  

Cremona's Diophantine Equations

American Journal of Mathematics, 1934
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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
Karen Aardal
exaly