Related papers: Kronecker-Weber via Stickelberger
This article describes a new proof of the equality condition for the Brunn-Minkowski inequality.
We prove the lemma of Knaster-Kuratowski-Mazurkiewicz as a consequence of the Lusternik-Schnirelman-Borsuk theorem.
We give a new proof of Lucas' Theorem in elementary number theory.
A one-line proof of a minimax theorem due to Steinerberger is given.
We prove a conjecture of Johann Cigler on shifted Hankel determinants.
Kronecker's 1856 paper contains a solvability theorem that is useful to construct unsolvable algebraic equations. We show how Kronecker's solvability theorem can be derived naturally via a polynomial complete decomposition method. This…
We give a new proof of a theorem of Mansour and Sun by using number theory and Rothe's identity.
Kolmogorov's invariant torus theorem is proved using a simple fixed point theorem.
We present in this work a new and simple proof of the false centre theorem.
Elementary proofs of Sylvester's, Wolstenholme's, Morley's and Lehmer's congruence theorems
This expository note presents a constructive proof of Wigner's theorem using only a few basic facts about Hilbert spaces, such as the existence of orthonormal bases and the Fourier decomposition of a vector. Our proof is based on a proof by…
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second…
We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.
We present several upper and lower bounds on the Kronecker coefficients of the symmetric group. We prove $k$-stability of the Kronecker coefficients generalizing the (usual) stability, and giving a new upper bound. We prove a lower bound…
We state and prove a new closure theorem closely related to the classical closure theorems of Poncelet and Steiner. Along the way, we establish a number of theorems concerning conic sections.
We give a new simpler proof of a theorem of Jayne and Rogers.
We give a new proof of the butterfly theorem, based on the use of several expressions involving the scale factor between the two wings.
This is a new version of our previous work. In this version, we fill a gap included in the original proof of Theorem 1.1 in our previous paper entitled "An iterative method for Kirchhoff type equations and its applications".
In this paper we give a complete proof of the Brumer-Stark conjecture over $\mathbf{Z}$.
We give a new proof of Glauberman's ZJ Theorem, in a form that clarifies the choices involved and offers more choices than classical treatments. In particular, we introduce two new ZJ-type subgroups of a $p$-group $S$, that contain…