Related papers: A simple proof of Zeeman's theorem
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…
We extract the Abhyankar-Moh-Suzuki theorem from the Lin-Zaidenberg theorem.
We provide a new simple and transparent proof of the version of Kummer's test given in [Tong, J. (1994). Amer. Math. Monthly. 101(5): 450--452]. Our proof is based on an application of a Hardy--Littlewood Tauberian theorem.
I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.
We present a proof of the Sturm-Hurwitz theorem, using basic calculus.
We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.
A proof of the Riemann hypothesis using the reflection principle is presented.
It is proved that Liouville theory and the two dimensional SO(2,1) gauged Wess-Zumino-Witten term are on-shell equivalent. This shed light on a possible higher dimensional generalization of the former theory.
We generalize and prove a result which was first shown by Zippin, and was explicitly formulated by Benyamini.
In this note, we present a simple directed graph proof of Sharkovsky's theorem.
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 paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
In measure theory, Steinhaus theorem is a result that deals with a property of the difference between two sets of positive measure. We give a simple elementary proof of the result.
In this paper, we give a detailed account of Goldfeld's proof of Siegel's theorem. Particularly, we present complete proofs of the nontrivial assumptions made in his paper.
In this note we will discuss Euler's solution of the simple difference equation that he gave in his paper{\it ``De serierum determinatione seu nova methodus inveniendi terminos generales serierum"} \cite{E189} (E189:``On the determination…
We give a generalization of Fujisawa's theorem in [F]. Our proof of the generalized theorem is purely algebraic and it is simpler than his proof.
We present some further results on Liouville type theorems for some conformally invariant fully nonlinear equations.
In this paper, we prove a Liouville theorem for the $2$-Hessian equation on the Heisenberg group $\mathbb{H}^n$. The result is obtained by choosing a suitable test function and using integration by parts to derive the necessary integral…
Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.
We study the triviality of the solutions of weighted superlinear heat equations on Riemannian manifolds with nonnegative Ricci tensor. We prove a Liouville--type theorem for solutions bounded from below with nonnegative initial data, under…