Related papers: A new proof of Lucas' Theorem

In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.

We give a short proof of Ahlfors' theorem on covering surfaces.

We present an astonishingly simple and elegant proof of the celebrated Basel problem.

In this paper, we provide new applications of Fibonacci and Lucas numbers. In some circumstances, we find algebraic structures on some sets defined with these numbers, we generalize Fibonacci and Lucas numbers by using an arbitrary binary…

An overlooked formula of E. Lucas for the generalized Bernoulli numbers is proved using generating functions. This is then used to provide a new proof and a new form of a sum involving classical Bernoulli numbers studied by K. Dilcher. The…

This note offers an elementary proof of the Siegel-Walfisz theorem for primes in arithmetic progressions.

In this article we will represent some ideas and a lot of new theorems in Euclidean plane geometry.

We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.

We introduce a class of group-like objects and prove that Cayley Theorem on groups has a counterpart in the class of group-like objects.

The paper gives a unified and simple proof of both theorems and Cousin's theorem.

We present a proof of a multidimensional version of Peres-Schlag's theorem on Diophantine approximations with lacunary sequences.

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].

We give an abstract approach to the results of Adams and Nobel, [1]. It allows to exhibit a new property of VC classes. It should be stressed that the basic ideas of proofs can be found in [1].

Boolos's proof of incompleteness is extended straightforwardly to yield simple ``diagonalization-free'' proofs of some classical limitative theorems of logic.

This note presents a proof of P\'olya's random walk theorem using classical methods from special function theory and asymptotic analysis.

We present a solution of Exercise 1.2.1 of [2] which yields a short new proof of a key step in one of proofs of Brouwer's fixed point theorem, 1910. A few people asked the author about the details of the solution and they might be…

This paper does three things: It proves a central limit theorem for novel permutation statistics (for example, the number of descents plus the number of descents in the inverse). It provides a clear illustration of a new approach to proving…

A proof of Sendov's conjecture is given.

Elementary proofs of unique factorization in rings of arithmetic functions using a simple variant of Euclid's proof for the fundamental theorem of arithmetic.