Fuchssche Gruppen, die freies Produkt zweier zyklischer Gruppen sind, und die Gleichung x2 + y2 + z2 = xyz.
Further remarks on Diophantine quintuples
A set of m positive integers with the property that the product of any two of them is the predecessor of a perfect square is called a Diophantine m-tuple. Much work has been done attempting to prove that there exist no Diophantine quintuples. In this paper we give stringent conditions that should be met by a putative Diophantine quintuple. Among others, we show that any Diophantine quintuple a,b,c,d,e with a < b < c < d < ed < 1.55·1072b < 6.21·1035c = a + b + 2√(ab+1) and ...
Gaussiana
Généralisation de la théorie des fractions continues
Generalization of a problem of Diophantus
Generalizations of Furtwängler's criteria for Fermat's last theorem and some related results.
Generalized ABC theorems for non-Archimedean entire functions of several variables in arbitrary characteristic
Generalized Frobenius numbers: bounds and average behavior
Generalized Lagrange criteria for certain quadratic Diophantine equations.
Generalized Vandermonde determinants
Generators and integer points on the elliptic curve y² = x³ - nx
Let E be an elliptic curve over the rationals ℚ given by y² = x³ - nx with a positive integer n. We consider first the case where n = N² for a square-free integer N. Then we show that if the Mordell-Weil group E(ℚ ) has rank one, there exist at most 17 integer points on E. Moreover, we show that for some parameterized N a certain point P can be in a system of generators for E(ℚ ), and we determine the integer points in the group generated by the point P and the torsion points. Secondly, we consider...
Generators and integral points on twists of the Fermat cubic
We study integral points and generators on cubic twists of the Fermat cubic curve. The main results assert that integral points can be in a system of generators in the case where the Mordell-Weil rank is at most two. As a corollary, we explicitly describe the integral points on the curve.
Géométrie d'Arakelov des variétés toriques et fibrés en droites intégrables
Groupes de Picard et problèmes de Skolem. I
Groupes de Picard et problèmes de Skolem. II
Hadamard products of certain power series
Halfway to a solution of
It is well known that the continued fraction expansion of readily displays the midpoint of the principal cycle of ideals, that is, the point halfway to a solution of . Here we notice that, analogously, the point halfway to a solution of can be recognised. We explain what is going on.
Hilbert's Tenth Problem for fields of rational functions over finite fields.
Homogeneous additive equations and Waring's problem
Homoroot integer numbers.