An explicit version of Birch's Theorem
An explicit version of Faltings' Product Theorem and an improvement of Roth's lemma
An exponential Diophantine equation related to the sum of powers of two consecutive k-generalized Fibonacci numbers
A generalization of the well-known Fibonacci sequence given by F₀ = 0, F₁ = 1 and for all n ≥ 0 is the k-generalized Fibonacci sequence whose first k terms are 0,..., 0, 1 and each term afterwards is the sum of the preceding k terms. For the Fibonacci sequence the formula holds for all n ≥ 0. In this paper, we show that there is no integer x ≥ 2 such that the sum of the xth powers of two consecutive k-generalized Fibonacci numbers is again a k-generalized Fibonacci number. This generalizes...
An exponential polynomial formed with the Legendre symbol
An extension of a result of C. J. Smyth to polynomials in several variables
An extension of a theorem of Duffin and Schaeffer in Diophantine approximation
Duffin and Schaeffer have generalized the classical theorem of Khintchine in metric Diophantine approximation in the case of any error function under the assumption that all the rational approximants are irreducible. This result is extended to the case where the numerators and the denominators of the rational approximants are related by a congruential constraint stronger than coprimality.
An extension of a theorem of Euler
An extension of a theorem of Nielsen
An extension of Bourgain and Garaev's sum-product estimates
An extension of Daykin's generalized Möbius function to unitary divisors.
An extension of Franklin's bijection.
An extension of Hansen's theorem for star chains.
An extension of Iwasawa's theorem on finitely generated modules over power series rings.
An extension of Mahler's theorem to simply connected nilpotent groups
This Note gives an extension of Mahler's theorem on lattices in to simply connected nilpotent groups with a -structure. From this one gets an application to groups of Heisenberg type and a generalization of Hermite's inequality.
An extension of -zeta function.
An extension of Schur's theorem on sum-free partitions
An extension of some formulae of Lerch
An extension of Sophie Germain's method to a wide class of diophantine equations.
An extension of the Apéry number supercongruence
An extension of the Khinchin-Groshev theorem
We prove a version of the Khinchin-Groshev theorem in Diophantine approximation for quadratic extensions of function fields in positive characteristic.