Related papers: A short proof of Combinatorial Nullstellensatz

We give an expository account of Nullstellensatz-like results when the base field is finite. In particular, we discuss the vanishing ideal of the affine space and of the projective space over a finite field. As an application, we include an…

In this article, using generalized derivations, we obtain a simple idea to prove the non-commutative Newton binomial formula in unital algebras and then, we extend that formula to non-unital algebras. Additionally, we establish the…

Let $f_i$ be polynomials in $n$ variables without a common zero. Hilbert's Nullstellensatz says that there are polynomials $g_i$ such that $\sum g_if_i=1$. The effective versions of this result bound the degrees of the $g_i$ in terms of the…

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

We prove the famous Faber intersection number conjecture and other more general results by using a recursion formula of $n$-point functions for intersection numbers on moduli spaces of curves. We also present some vanishing properties of…

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

We prove the strong form of the Gaussian product conjecture in dimension three. Our purely analytical proof simplifies previously known proofs based on combinatorial methods or computer-assisted methods, and allows us to solve the case of…

The Schm\"udgen's Positivstellensatz gives a certificate to verify positivity of a strictly positive polynomial $f$ on a compact, basic, semi-algebraic set $\mathbf{K} \subset \mathbb{R}^n$. A Positivstellensatz of this type is called…

In this very short note, we give a counterexample to a recent conjecture of Gilmer which would have implied the union-closed conjecture.

In this short exposition we provide a simplified proof of Buser's result for Cheeger's isoperimetric constant.

This article provides a simple proof of the quadratic formula, which also produces an efficient and natural method for solving general quadratic equations. The derivation is computationally light and conceptually natural, and has the…

In this paper, we will give a new proof for a known result of the mean square of Riemann zeta-function.

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 note, we give examples that demonstrate a negative answer to the generalized numerical criterion problem for pairs.

We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…

These notes are a self-contained short proof of the stability of persistence diagrams.

We produce a new, shorter construction of a minor-universal planar graph.

In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.

I want to show one possibility to proof the Collatz conjecture, also called 3n+1 conjecture, for any natural number N. For this, I limit my analysis on the direct odd follower of every natural odd number and show the connections between the…

We prove an infinitary version of the Brauer-Schur theorem.