Related papers: Two conjectures on integer arithmetic and their ap…
The paper was withdrawn by the author. It contained various errors.
This paper has been withdrawn by the author, due to errors in Groebner basis calculations in the cases of five and six dimensional groups.
This paper has been withdrawn by the authors, due a crucial mistake in Lemma 2
In this paper we give solutions of certain diophantine equations related to triangular and tetrahedral numbers and propose several problems connected with these numbers. The material of this paper was presented in part at the 11th…
This paper has been withdrawn by the authors due to an unlikely results.
This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.
In this paper we present a new approach to prove effective results in Diophantine approximation. We then use it to prove an effective theorem on the simultaneous approximation of two algebraic numbers satisfying an algebraic equation with…
This paper has been withdrawn by the author due to a gap in the proof of the main result.
We announce a number of conjectures associated with and arising from a study of primes and irrationals in $\mathbb{R}$. All are supported by numerical verification to the extent possible.
This paper has been withdrawn by the author due to an error in the computation of E(n,x) on page 6 which appears to be essential for the result. The author is currently trying to correct this proof
This paper has been withdrawn because Proposition 2.2 (c) is false. This invalids the main results of section 2 and 3. We thank A. Canonaco for pointing us the error.
The said paper [Su2] entitled "Proof Of Two Dimensional Jacobian Conjecture" is false.
This paper has been withdrawn by the author(s), due to a crucial error in eq. 6.
This paper has been withdrawn by the author due to a crucial error
The paper is withdrawn because the analysis appeared to be incomplete.
The results of several papers concerning the \v{C}ern\'y conjecture are deduced as consequences of a simple idea that I call the averaging trick. This idea is implicitly used in the literature, but no attempt was made to formalize the proof…
This paper has been withdrawn by the authors. Because of a misunderstanding, the paper was submitted prematurely to the arXiv. A replacement will follow.
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…
The main goal of this note is to develop a metrical theory of Diophantine approximation within the framework of the de Mathan-Teulie Conjecture, also known as the `Mixed Littlewood Conjecture'. Let p be a prime. A consequence of our main…
The paper is withdrawn. The reviewer pointed out that the assertion that the quantity $D_{\Gamma}$ is finite (used by the author) is still unproved for the general group, and perhaps is false.