All elite primes up to 250 billion.
All Generalized Morse-Sequences are Loosely Bernoulli.
All Liouville Numbers are Transcendental
In this Mizar article, we complete the formalization of one of the items from Abad and Abad’s challenge list of “Top 100 Theorems” about Liouville numbers and the existence of transcendental numbers. It is item #18 from the “Formalizing 100 Theorems” list maintained by Freek Wiedijk at http://www.cs.ru.nl/F.Wiedijk/100/. Liouville numbers were introduced by Joseph Liouville in 1844 [15] as an example of an object which can be approximated “quite closely” by a sequence of rational numbers. A real...
All Two-Gnerator Fuchsian Group.
Alle großen ganzen Zahlen lassen sich als Summe von höchstens 71 Primzahlen darstellen
Allgemeine Theorie der kettenbruchähnlichen Algorithmen, in welchen jede Zahl aus drei vorhergehenden gebildet wird.
Almost all short intervals containing prime numbers
Almost -representation. (Presque -représentations.)
Almost Constant Sequences and Well-Distribution in Compact Groups.
Almost Constant Sequences of Transformations.
"Almost every" algebraic number-field has a large class-number
Almost perfect powers in arithmetic progression
Almost perfect powers in consecutive integers
Almost periodic functions and uniform distribution mod 1.
Almost periodic sequences and functions with given values
We present a method for constructing almost periodic sequences and functions with values in a metric space. Applying this method, we find almost periodic sequences and functions with prescribed values. Especially, for any totally bounded countable set in a metric space, it is proved the existence of an almost periodic sequence such that and , for all and some which depends on .
Almost periodicity of some error terms in prime number theory
Almost powers in the Lucas sequence
The famous problem of determining all perfect powers in the Fibonacci sequence and in the Lucas sequence has recently been resolved [10]. The proofs of those results combine modular techniques from Wiles’ proof of Fermat’s Last Theorem with classical techniques from Baker’s theory and Diophantine approximation. In this paper, we solve the Diophantine equations , with and , for all primes and indeed for all but primes . Here the strategy of [10] is not sufficient due to the sizes of...
Almost primality of group orders of elliptic curves defined over small finite fields.
Almost product evaluation of Hankel determinants.
Almost regular quaternary quadratic forms
We investigate the almost regular positive definite integral quaternary quadratic forms. In particular, we show that every such form is -anisotropic for at most one prime number . Moreover, for a prime there is an almost regular -anisotropic quaternary quadratic form if and only if . We also study the genera containing some almost regular -anisotropic quaternary form. We show several finiteness results concerning the families of these genera and give effective criteria for almost regularity....