Related papers: Two conjectures on integer arithmetic and their ap…

This paper has been withdrawn.

This paper has been withdrawn by the authors due to an error.

We prove a generalization of W.M. Schmidt's theorem related to the Diophantine approximations for a linear form of the type $\alpha_1x_1+\alpha_2x_2 +y$ with {\it positive} integers $x_1,x_2$.

This paper has been withdrawn by the author due to the unsure solution to the Dyson-Schwinger equation.

This paper has been withdrawn by the author due to a serious mistake on Lemma 2.4.

This paper has been withdrawn by the author(s), due a mistake of factor 1/2.

The paper has been withdrawn by the author, due to a critical error stemming from the defined template.

We consider a variety of Euler's conjecture, i.e., whether the Diophantine system \[\begin{cases} n=a_{1}+a_{2}+\cdots+a_{s-1}, a_{1}a_{2}\cdots a_{s-1}(a_{1}+a_{2}+\cdots+a_{s-1})=b^{s} \end{cases}\] has solutions…

This paper has been withdrawn by the author due to a crucial error in the Proof of Theorem 0.3

This paper has been withdrawn because the result turns out to be trivial.

This submission has been withdrawn by arXiv admins due to fraudulent affiliation claims by the original submitter.

This paper has been withdrawn.

We withdraw this paper due to insufficient arguments in the derivation of Theorem 1. See quant-ph/0005062 for the new paper

This paper is withdrawn because the results in the paper are included in a paper to be published in Mathematical and Computer Modelling.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, the abc conjecture is negated under certain conditions

This paper has been withdrawn by the author, due to a crucial error in the proof of Thm.1

This paper has been withdrawn by the author due to an error in section 7. There is a new version: arXiv:1011.3352.

This paper has been withdrawn by arXiv administrators because of disputed claims of authorship among former collaborators

There have been gaps found in the proofs. The paper is withdrawn until further notice.

Paper withdrawn because of a gap in the proof of Proposition 3 of Thomas Schick: "Integrality of L2-Betti numbers", Math. Ann. 317, 727-750 (arXiv.org/abs/math.gt/0001101). Most results of the withdrawn paper were based on this proposition.