منابع مشابه
On a Quartic Diophantine Equation
The wish to determine the complete set of rational integral solutions of (1) was expressed by Diaconis and Graham in [2, p. 328]. Apparently, the solutions to this diophantine problem correspond to values of keN for which the Radon transform based on the set of all xeZ\ with exactly four ones is not invertible. We thank Hendrik Lenstra who communicated the problem to Jaap Top, to whom we are eq...
متن کاملOn Two-Parametric Quartic Families of Diophantine Problems
Let n ≥ 3, v1(x), . . . , vn−1(x) ∈ Z[x] and u ∈ {−1, 1}, then x(x− v1(a)y) · · · (x− vn−1(a)y) + uy = ±1 is called a parametrized familiy of Thue equations, if a ∈ Z and the solutions x, y are searched in Z; cf. Thomas (1993). There are several results concerning parametrized families of cubic and quartic families of Thue equations, see Mignotte et al. (1996) and the references therein. Thomas...
متن کاملA Generalization of a Theorem of Bumby on Quartic Diophantine Equations
Given a parametrized family of cubic models of elliptic curves Et over Q, it is a notoriously difficult problem to find absolute bounds for the number of integral points on Et (and, indeed, in many cases, it is unlikely such bounds even exist). Perhaps somewhat surprisingly, the situation is often radically different for quartic models. In a series of classical papers, Ljunggren (see e.g. [5] a...
متن کاملDiophantine approximation and Diophantine equations
The first course is devoted to the basic setup of Diophantine approximation: we start with rational approximation to a single real number. Firstly, positive results tell us that a real number x has “good” rational approximation p/q, where “good” is when one compares |x − p/q| and q. We discuss Dirichlet’s result in 1842 (see [6] Course N◦2 §2.1) and the Markoff–Lagrange spectrum ([6] Course N◦1...
متن کاملDetailed Examination of Transport Coefficients in Cubic-Plus-Quartic Oscillator Chains
We examine the thermal conductivity and bulk viscosity of a onedimensional (1D) chain of particles with cubic-plus-quartic interparticle potentials and no on-site potentials. This system is equivalent to the FPUαβ system in a subset of its parameter space. We identify three distinct frequency regimes which we call the hydrodynamic regime, the perturbative regime and the collisionless regime. In...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 2007
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa128-4-3