Related papers: A new proof of Vantieghem's theorem
We recast Euclid's proof of the infinitude of prime numbers as a Euclidean Criterion for a domain to have infinitely many atoms. We make connections with Furstenberg's "topological" proof of the infinitude of prime numbers and show that our…
We give a new, elementary proof of the celebrated Herzog-Hibi-Zheng theorem on powers of quadratic monomial ideals.
We give a new proof of Lucas' Theorem in elementary number theory.
We prove some theorems which give sufficient conditions for the existence of prime numbers among the terms of a sequence which has pairwise relatively prime terms.
In this note we generalise a method of Perott to give new proofs that there are infinitely many prime numbers.
This document presents an alternative proof of Sylvester's theorem stating that "the product of $n$ consecutive numbers strictly greater than $n$ is divisible by a prime strictly greater than $n$". In addition, the paper proposes stronger…
We present a new proof of the celebrated quadratic reciprocity law. Our proof is based on group theory.
We give a new simpler proof of a theorem of Jayne and Rogers.
We generalize and prove a result which was first shown by Zippin, and was explicitly formulated by Benyamini.
Inspired by a recent preprint of N. Curien, we provided what may be a new and elementary proof of the Law of Large Numbers.
We present a self-contained elementary and detailed exposition of Mertens' own proof of his theorem on the divergence of the series of the reciprocals of the primes and compare it with the modern proofs. His proof contains explicit…
We put a new conjecture on primes from the point of view of its binary expansions and make a step towards justification.
In 1737 Leonard Euler gave what we often now think of as a new proof, based on infinite series, of Euclid's theorem that there are infinitely many prime numbers. Our short paper uses a simple modification of Euler's argument to obtain new…
I give some claims on primorial prime numbers for interested readers in number theory.
While the prime numbers have been subject to mathematical inquiry since the ancient Greeks, the accumulated effort of understanding these numbers has - as Marcus du Sautoy recently phrased it - 'not revealed the origins of what makes the…
I present a proof of the quantum probability rule from decision-theoretic assumptions, in the context of the Everett interpretation. The basic ideas behind the proof are those presented in Deutsch's recent proof of the probability rule, but…
Polynomial time primality tests for specific classes of numbers of the form $k\cdot 2^m \pm 1$ are introduced.
We recall Charles Babbage's 1819 criterion for primality, based on simultaneous congruences for binomial coefficients, and extend it to a least-prime-factor test. We also prove a partial converse of his non-primality test, based on a single…
This note offers an elementary proof of the Siegel-Walfisz theorem for primes in arithmetic progressions.
We give a new proof of Vassiliev's planarity criterion for framed four-valent graphs (and more generally, *-graphs), which is based on Pontryagin-Kuratowski theorem.