Related papers: Conditional Negation of The abc Conjecture
The paper presents a counterexample to the Hodge conjecture.
In this article, we give two different proofs of why the Collatz Conjecture is false.
In this paper, we give a simple counter example to the famous Hodge conjecture.
This note imparts heuristic arguments and theorectical evidences that contradict the abc conjecture over the rational numbers. In addition, the rudimentary datails for transforming this problem into the doimain of equidistribution theory…
We revisit a subexponential bound for the $abc$ conjecture due to the first author, and we establish a variation of it using linear forms in logarithms. As an application, we prove an unconditional subexponential bound towards the $4$-terms…
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.
Nous refutons, sous une certaine hypothese combinatoire, la "nonrevisiting path conjecture". Abstract: In this article, we give, under some hypothesis, a couterexample to the nonrevisiting path conjecture.
This paper describes a method used to construct infinitely many probable counterexamples of the abc conjecture over the rational integers.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
In this paper, we give a form of refined Roth's theorem. As an application, we prove a special case of the $abc$-conjecture.
Ellenberg proved that the abc conjecture would follow if this conjecture were known for sums $a+b=c$ such that $D\mid abc$ for some integer~$D$. Mochizuki proved a theorem with an opposite restriction, that the full abc conjecture would…
This note analyzes in terms of categorial proof theory some standard assumptions about negation in the absence of any other connective. It is shown that the assumptions for an involutive negation, like classical negation, make a kind of…
In this paper, we give a counter-example, in the general case, Kronecker theorem will derive contradiction. Kronecker theorem be correct after removing some conditions.
We show that the abc Conjecture implies the Weak Diversity Conjecture of Bilu and Luca.
The conjecture of Masser-Oesterl\'e, popularly known as $abc$-conjecture have many consequences. We use an explicit version due to Baker to solve a number of conjectures.
This paper is cancelled
In this paper we consider the remaining cases of Hebey-Vaugon conjecture.
In this paper, we state a conjecture on the prime factorization of numbers of the form $n!+1$, explore its implications, and compare it with empirical evidence and established results based on the $abc$ conjecture.
The article presents the proof of Casas-Alvero conjecture.
This paper has been withdrawn by the author, due an error in the proof of Proposion 2.13.