Related papers: Casas-Alvero Conjecture is true
In this paper, we give a survey of the recent develpoments of the DDVV conjecture.
We provide a short proof of the 1-dimensional flat chain conjecture.
We study varieties defined by parameterizing polynomials of derivatives through a computational algebro-geometric approach, especially relying on Combinatorial Nullstellensatz and Noether normalization. We establish that these polynomials…
The paper gives a unified and simple proof of both theorems and Cousin's theorem.
We extend Carpi's results by showing that Dejean's conjecture holds for n >= 30.
We give a proof of Brooks' theorem and its list coloring extension using the algebraic method of Alon and Tarsi; this also shows that the Brooks' theorem remains valid in a more general game coloring setting.
In this note, while giving an overview of the state of art of the well known Hadamard conjecture, which is more than a century old and now it has been established by using the methods given in the two papers by Mohan et al [6,7].
In this article, we give two different proofs of why the Collatz Conjecture is false.
In this paper, we bring a complete solution to the Ovals problem, as formulated in [3] and [24].
We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
The paper contains a proof of the Fontaine-Jannsen conjecture based on a crystalline version of the p-adic Poincar'e lemma (different proofs were found earlier by Faltings, Niziol and Tsuji).
A conjecture is given that, if true, could lead to an algorithm for computing definite sums of rational functions.
We prove a variation of Gronwall's lemma.
We present the proofs of the conjectures mentioned in the paper published in the proceedings of the 2024 AAAI conference [1], and discovered by the decomposition methods presented in the same paper.
We introduce a new criterion which if satisfied implies the Riemann hypothesis.
In this work, the q-analogue of Bernoulli inequality is proved. Some other related results are presented.
In this work we resolve several conjectures stated in the On-Line Encyclopedia of Integer sequences.
We give a short proof of Ahlfors' theorem on covering surfaces.
We give a new proof of Lucas' Theorem in elementary number theory.