Equations in roots of unity
Equations involving arithmetic functions of factorials.
Equations relating factors in decompositions into factors of some family of plane triangulations, and applications (with an appendix by Andrzej Schinzel)
Let be the family of all 2-connected plane triangulations with vertices of degree three or six. Grünbaum and Motzkin proved (in dual terms) that every graph P ∈ has a decomposition into factors P₀, P₁, P₂ (indexed by elements of the cyclic group Q = 0,1,2) such that every factor consists of two induced paths of the same length M(q), and K(q) - 1 induced cycles of the same length 2M(q). For q ∈ Q, we define an integer S⁺(q) such that the vector (K(q),M(q),S⁺(q)) determines the graph P (if P is...
Equirépartition des solutions du problème de Waring
Errata-Corrige : “The Mordell conjecture revisited”
Erweiterung dreielementiger Basen bei konstanter Frobeniuszahl.
Estimates for reduced binary forms.
Étude bibliographique. Sur la théorie des nombres
Étude sur la théorie des résidus cubiques.
Étude sur les décompositions en sommes de deux carrés, du carré d’un nombre entier composé de facteurs premiers de la forme , et de ce nombre lui-même. Formules et application à la résolution complète, en nombres entiers, des équations indéterminées, simultanées, et (fin)
Étude sur les décompositions en sommes de deux carrés, du carré d’un nombre entier composé de facteurs premiers de la forme , et de ce nombre lui-même. Formules et application à la résolution complète, en nombres entiers, des équations indéterminées, simultanées, et
Euler's concordant forms
Exact m-covers and the linear form
Exceptional units and numbers of small Mahler measure.
Expansions of binary recurrences in the additive base formed by the number of divisors of the factorial
We note that every positive integer N has a representation as a sum of distinct members of the sequence , where d(m) is the number of divisors of m. When N is a member of a binary recurrence satisfying some mild technical conditions, we show that the number of such summands tends to infinity with n at a rate of at least c₁logn/loglogn for some positive constant c₁. We also compute all the Fibonacci numbers of the form d(m!) and d(m₁!) + d(m₂)! for some positive integers m,m₁,m₂.
Explicit complete solution in integers of a class of equations (ax2 -b)(ay2-b) = z2 - c.
Explicit solution of a class of quartic Thue equations
Expressing rationals as a sum of a small number of unit fractions
Extensions of some parametric families of -triples.
Extensions of Three Theorems of Nagell
Three theorems of Nagell of 1923 concerning integer values of certain sums of fractions are extended.