Related papers: A new proof of Lucas' Theorem
In this expository article we provide an elegant proof of the one-sided Ingham-Karamata Tauberian theorem. As an application, we present a short deduction of the prime number theorem.
The Taylor expansion is a widely used and powerful tool in all branches of Mathematics, both pure and applied. In Probability and Mathematical Statistics, however, a stronger version of Taylor's classical theorem is often needed, but only…
Sury's 2014 proof of an identity for Fibonacci and Lucas numbers (Identity 236 of Benjamin and Quinn's 2003 book: {\em Proofs that count: The art of combinatorial proof}) has excited a lot of comment. We give an alternate, telescoping,…
We prove a result on the existence of linear forms of a given Diophantine type.
In this note, we establish some new results on some special types of function algebras and also give new proofs to some existing ones
I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.
This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.
We announce numerous new results in the theory of orthogonal polynomials on the unit circle.
The aim of this paper is to prove a version of Lie's theorem for the supertropical algebra.
We produce a new, shorter construction of a minor-universal planar graph.
This paper provides a proof of a LLT-like test for Fermat numbers, based on the properties of Lucas Sequences and on the method of Lehmer.
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
In this paper, we obtain analogues of Zsigmondy's theorem and the primitive divisor results for the Lucas and Lehmer sequences in polynomial rings of several variables.
Lucas-Lehmer test is the current standard algorithm used for testing the primality of Mersenne numbers, but it may have limitations in terms of its efficiency and accuracy. Developing new algorithms or improving upon existing ones could…
This paper highlights the emergence of the Omega sequence in number theory and its connection with the emergence of a new prime number, and also highlights its theoretical applications for Lucas-Lehmer primality test, and Euclid-Euler…
We prove an infinitary version of the Brauer-Schur theorem.
We prove a variation of Gronwall's lemma.
We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.
We improve the previuosly known bound for some vertex Folkman numbers.
Repdigits are natural numbers formed by the repetition of a single digit. In this paper, we study the problem of writing repdigits as the difference of two balancing or Lucas-balancing numbers. The method of proof involves the application…