Related papers: Two conjectures on integer arithmetic and their ap…
Although the results are correct, it was pointed out that the results follow from some previously known results. Accordingly, this version of the paper is withdrawn by the authors.
This paper has been withdrawn by the authors, since it has been merged with Part I (ID 0802.3570)
Major mistake. The paper has been withdrawn.
The problem of finding perfect Euler cuboids or proving their non-existence is an old unsolved problem in mathematics. The second cuboid conjecture is one of the three propositions suggested as intermediate stages in proving the…
This paper has been withdrawn by the author, due to a crucial error in the proof of Lemma 3.1.
A detailed survey of the Lonely Runner Conjecture and its connection between Diophantine approximation and View-obstruction problems.
Let $\mathcal{D}=(d_n)_{n=1}^\infty$ be a bounded sequence of integers with $d_n\ge 2$ and let $(i, j)$ be a pair of strictly positive numbers with $i+j=1$. We prove that the set of $x \in \RR$ for which there exists some constant $c(x) >…
This paper has been withdrawn because of serious errors.
We prove a strong simultaneous Diophantine approximation theorem for values of additive and multiplicative functions provided that the functions have certain regularity on the primes.
This paper has been withdrawn due to a crucial error in the proof of the main theorem
We are motivated by a result of Alzer and Luca who presented all the integer solutions to the relations $(k!)^n-k^n=(n!)^k-n^k$ and $(k!)^n+k^n=(n!)^k+n^k$. We modify the equations by considering the double factorial instead and present all…
This paper has been withdrawn due to a crucial theoretical and experimental error.
This paper is withdrawn. We found a mistake in Lemma 4.1
The main goal of this paper is to introduce a set of conjectures on the relations in the tautological rings. In particular, the framework gives an efficient algorithm to calculate all tautological equations using only finite dimensional…
Withdrawn paper because the results are published in math.AT/0308054 and math.AT/0308063.
This paper has been withdrawn.
This paper has been withdrawn by the authors
Some divergent trigonometric integrals have appeared in standard tables for many years, listed as converging. We give a simple proof that these integrals diverge and trace their history. The original error was made when a (startlingly)…
Using algebraic transformations and equivalent reformulations we derive a number of new results from some earlier ones (by the author) in more accepted terms closely related to well-known conjectures of Bondy and Jung including a number of…
The paper has been withdrawn by the author.