Related papers: A simple proof of a conjecture on univariate polyn…
This paper has been withdrawn due to a crucial error in the proof of the main theorem
This paper has been withdrawn by the author due to a critical error in the proof of Theorem A pointed out by Burkhard Wilking.
This paper has been withdrawn by the author due to a crucial error.
This article is withdrawn because of a mistake in the main result of the paper.
This paper has been withdrawn by the author due to an error.
In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…
This paper has been withdrawn by the authors because the paper is largely revised and improved, and to appear in Mechanics Research Communications.
This paper has been withdrawn by the authors due to its publication
The paper has been withdrawn due to a crucial error in section 3.
The main result of this paper, Simon's conjecture for fibered knots, was previously proven by Silver and Whitten math.GT/0405462 with essentially the same proof. This paper is therefore being withdrawn. The author would like to apologize…
This paper has been withdrawn by the author, due to a crucial error in the proof of Thm.1
We establish necessary and sufficient conditions for an arbitrary polynomial of degree $n$, especially with only real roots, to be trivial, i.e. to have the form a(x-b)^n. To do this, we derive new properties of polynomials and their roots.…
This paper has been withdrawn by the author due to an error.
This paper has been withdrawn by the author because there are some typos in proofs.
This paper has been withdrawn by the author.
This paper has been withdrawn due to a crucial theoretical error.
This paper has been withdrawn by the author due to an error in the proof.
The Casas-Alvero conjecture states: if a complex univariate polynomial has a common root with each of its derivatives, then it has a unique root. We show that hypothetical counterexamples must have at least 5 different roots. The first case…
This submission has been withdrawn at the request of the author.
The Casas--Alvero conjecture predicts that every univariate polynomial $f$ over a field $K$ of characteristic zero having a common factor with each of its derivatives $H\_i(f)$ is a power of a linear polynomial. Let…