Related papers: A new proof of Lucas' Theorem

We present a new, elementary, dynamical proof of the prime number theorem.

We prove a Lucas-type congruence for q-Delannoy numbers.

We prove an infinite family of lacunary recurrences for the Lucas numbers using combinatorial means.

We give elementary proofs of some congruence criteria to compute binomial coefficients in modulo a prime. These criteria are analogues to the symmetry property of binomial coefficients. We give extended version of Lucas Theorem by using…

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

We present in this work a new and simple proof of the false centre theorem.

We give a new simpler proof of a theorem of Jayne and Rogers.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

We give a new elementary proof of Landau's Prime Ideal Theorem. The proof is an extension of Richter's proof of the Prime Number Theorem. The main result contains other results related to the equidistribution of the prime ideal counting…

An technically interesting proof of a known theorem.

We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…

We give a counting based proof of the Graham Pollak Theorem

We give an elementary proof to Hasse theorem.

In this note we shall give a new proof to a quadrature formulae due to Newton.

We give here a new proof of a Tauberian Theorem of complex Laplace transform using the Theory of measure and theory of function with bounded variations. However we deduce the simple proof of Prime Number Theorem.

We show that an elementary proof of Fermat's Last Theorem (FLT) exists. Our paper also extends the scope of FLT from integers to all rational numbers.

In this note we give two proofs of Brooks' Theorem. The first is obtained by modifying an earlier proof and the second by combining two earlier proofs. We believe these proofs are easier to teach in Computer Science courses.

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

We present a new topological proof of the infinitude of prime numbers with a new topology. Furthermore, in this topology, we characterize the infinitude of any non-empty subset of prime numbers.

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.