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We give a new proof of the fundamental theorem of algebra. It is entirely elementary, focused on using long division to its fullest extent. Further, the method quickly recovers a more general version of the theorem recently obtained by…

A generalization of the law of total covariance is presented and proved.

We generalize Romanoff's theorem. Also, we obtain a result on sums related to Euler's totient function.

We give a proof for the fundamental theorem of algebra,using the Fredholm index phenomena

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

We generalize [3, Lemma 2.2] and [4, Proposition 2.3] and deduce a positive result on Hilbert's fourteenth problem. Further, we give a relatively transparent and elementary proof of [3, Theorem 1.1].

In this note, we present a simple directed graph proof of Sharkovsky's theorem.

Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…

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…

We present a self-contained combinatorial approach to Fujita's conjectures in the toric case. Our main new result is a generalization of Fujita's very ampleness conjecture for toric varieties with arbitrary singularities. In an appendix, we…

We present an elementary proof of Fermat's Last Theorem. No ancillary results are used, not even the most basic ones. The proof directly leads to a contradiction of the Fermat equation in the set of integers.

A theorem due to Ohkawa states that the collection of Bousfield equivalence classes of spectra is a set. We extend this result to arbitrary combinatorial model categories.

We prove a generalization of one of Lie's Theorems in the context of Lie-like algebras$^{2-nd}$.

We show that Fueter's theorem holds for a more general class of quaternionic functions than those constructed by the Fueter's method.

In this paper, we give a more physical proof of Liouville's theorem for a class generalized harmonic functions by the method of parabolic equation.

In this paper, we propose a generalization of a congruence due to Carlitz.

We give a proof of Iitaka's Conjecture C_{2,1} using only elementary methods from algebraic geometry. The main point is that, given a non-isotrivial and relatively minimal family f : X \to B, where X is a surface and B is a curve, both…

The recently developed proof of Fermat's Last Theorem is very lengthy and difficult, so much so as to be beyond all but a small body of specialists. While certainly of value in the developments that resulted, that proof could not be, nor…

It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.

In this paper we review a general proof for the irrationality property of numbers which take a certain form of infinite sums.