Related papers: A proof of Dejean's conjecture

We extend Carpi's results by showing that Dejean's conjecture holds for n >= 30.

We show that Dejean's conjecture holds for n>=27. This brings the final resolution of the conjecture by the approach of Moulin Ollagnier within range of the computationally feasible.

We prove Union-Closed sets conjecture.

We establish a lower bound for the size of possible counterexamples of the Dixmier Conjecture. We prove that $B>15$, where $B$ is the minimum of the greatest common divisor of the total degrees of $P$ and $Q$, where $(P,Q)$ runs over the…

The union-closed sets conjecture (Frankl's conjecture) says that for any finite union-closed family of finite sets, other than the family consisting only of the empty set, there exists an element that belongs to at least half of the sets in…

Consider the set of all natural numbers that are co-prime to primes less than or equal to a given prime. Then given a consecutive pair of numbers in that set with an arbitrary even gap, we prove there exists an unbounded number of actual…

We prove the Aharoni Berger Conjecture

Let the root of the word $w$ be the smallest prefix $v$ of $w$ such that $w$ is a prefix of $vvv...$. $per(w)$ is the length of the root of $w$. For any $n\ge5$, an $n$-ary threshold word is a word $w$ such that for any factor (subword) $v$…

We survey recent developments on the Restriction conjecture.

We provide new sufficient conditions under which Ryser's conjecture holds.

We prove that at least $\left( \dfrac{(1+\epsilon)2m}{N-1}+1+\epsilon \right)^N$, where $0\leqslant \epsilon <1$, many general points, satisfy Demailly's conjecture. Previously, it was known to be true for at least $(2m+2)^N$ many general…

In this paper, we prove the conjecture that if there is an odd perfect number, then there are infinitely many of them.

We will prove the Brannan conjecture for particular values of the parameter. The basic tool of the study is an integral representation published in a recent work [3].

Several results about the union-closed sets conjecture are presented.

Levin's conjecture has been established to hold true for group equations of length up to seven. Recently, it is shown that Levin's conjecture is also true (modulo exceptional cases) for some group equations of length eight and nine. In this…

Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.

We analyze a possible minimal counterexample to the Jacobian Conjecture $P,Q$ with $\gcd(deg(P),deg(Q))=16$ and show that its existence depends only on the existence of solutions for a certain Abel differential equation of the second kind.

In the paper we complete a case by case proof of Reeder's Conjecture started in our previous work, proving the conjecture for simple Lie algebras of type $D$ and for the exceptional cases.

Based on the first 25 known values of Pi(10^n), the number of primes less than 10^n, with n integer between 1 and 25, we propose a conjectured value range of Pi(10^26) calculated by using polynomial interpolations with two corrective…

The Ramanujan Machine project predicts new continued fraction representations of numbers expressed by important mathematical constants. Generally, the value of a continued fraction is found by reducing it to a second order linear difference…