Related papers: A new proof of Lucas' Theorem

This note gives an elementary exposition of a variant of the spread polynomials in terms of Fibonacci and Lucas polynomials.

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

We give an elementary proof of a Landesman-Lazer type result for systems by means of a shooting argument and explore its connection with the fundamental theorem of algebra.

We prove a central limit theorem with aassumptions which are many weak than classical conditions

We prove a uniformization theorem in complex algebraic geometry.

We prove some new results related to Tanaka's formula.

We provide a simple and short proof of the Karush-Kuhn-Tucker theorem with finite number of equality and inequality constraints. The proof relies on an elementary linear algebra lemma and the local inverse theorem.

We establish some new theorems on pentagon and pentagram.

We settle in the affirmative the Graham-Sloane conjecture.

In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.

In this article using elementary school level Geometry we observe an alternative proof of Pythagorean Theorem from Heron's Formula.

We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.

In 1878 \'E. Lucas proved a remarkable result which provides a simple way to compute the binomial coefficient ${n\choose m}$ modulo a prime $p$ in terms of the binomial coefficients of the base-$p$ digits of $n$ and $m$: {\it If $p$ is a…

In this note we give a detailed proof of a theorem of Aubin.

Positive integers with all digits equal are called repdigits. In this paper, we find all balancing and Lucas-balancing numbers, which can be expressed as the difference of two repdigits. The method of proof involves the application of…

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

By using the elementary symmetric polynomials and some results of number theory, we solve the well known problem of Lehmer on Euler's totient function. As application, we obtain a new characterization of prime numbers.

We introduce an elementary argument to the theory of distribution of sequences modulo one.

We illustrate the concept of mathematical proof.

Recent developments in the categorical foundations of universal algebra have given fresh impetus to an understanding of the lambda calculus coming from categorical logic: an interpretation is a semi-closed algebraic theory. Scott's…