Related papers: Geometrical Equivalents of Goldbach Conjecture and…
In this short paper we propose four conjectures in synthetic geometry that generalize Erdos-Mordell Theorem, and three conjectures in number theory that generalize Fermat Numbers.
This paper presents some considerations about the Goldbach's conjecture (GC). The work is based on elementary results of the number theory and it provides a constructive method that permits, given an even integer, to find at least a pair of…
We establish an analogue of the Goldbach conjecture for Laurent polynomials with positive integer coefficients.
We study two conjectures in additive combinatorics. The first is the polynomial Freiman-Ruzsa conjecture, which relates to the structure of sets with small doubling. The second is the inverse Gowers conjecture for $U^3$, which relates to…
We present a formulation of the Collatz conjecture that is potentially more amenable to modeling and analysis by automated termination checking tools.
An approximate formula for the partitions of Goldbach's Conjecture is derived using Prime Number Theorem and a heuristic probabilistic approach. A strong form of Goldbach's conjecture follows in the form of a lower bounding function for the…
In this paper a new conjecture equivalent to Collatz conjecture is presented. In particural, showing that (all) the solution(s) of newly introduced iterative functional equation(s) have a given property is equivalent to prove Collatz…
According to some discussions based on syllogism, we present results on the binary Goldbach conjecture in three categories: results that are weaker than the Goldbach conjecture, sufficient conditions for the Goldbach conjecture, and results…
According to the similarity theorem on the distributions of the effective prime factors and by using two-part method, Goldbach theorem and, consequently, Goldbach conjecture was proved.
Multiplicative arithmetic functions satisfying the parallelogram functional equation on prime numbers are investigated. It is derived that the unique solution is a quadratic function by the Goldbach's conjecture.
We construct two Frechet algebras admitting countably many mutually inequivalent Frechet algebra topologies. The second example is a modification of the maiden (and first) example of a non-Banach Frechet algebra with two inequivalent…
In this paper we obtain new sets of equivalents of the Fermat-Wiles theorem. Simultaneously, we obtain also asymptotic connections between the set of Dirichlet's series, certain segments of the Dirichlet's sum $\mfrak{D}(x)$, Riemann…
In this paper we propose an alternative formulation of the binary and ternary Goldbach conjectures as the systems of equations involving the Euler $\phi$-function.
The celebrated Mirror Theorem states that the genus zero part of the A model (quantum cohomology, rational curves counting) of the Fermat quintic threefold is equivalent to the B model (complex deformation, variation of Hodge structure) of…
In this paper we propose counterexamples to the Geometrization Conjecture and the Elliptization Conjecture.
We introduce a collection of polynomials $F_N$, associated to each positive integer $N$, whose divisibility properties yield a reformulation of the Goldbach conjecture. While this reformulation certainly does not lead to a resolution of the…
For orbifolds admitting a crepant resolution and satisfying a hard Lefschetz condition, we formulate a conjectural equivalence between the Gromov-Witten theories of the orbifold and the resolution. We prove the conjecture for the…
We propose a 'geometric Chevalley-Warning' conjecture, that is a motivic extension of the Chevalley-Warning theorem in number theory. It is equivalent to a particular case of a recent conjecture of F. Brown and O.Schnetz. In this paper, we…
"Goldbach's Conjecture" proven by analysis of how all combinations of the odd primes, summed in pairs, generates all of the even numbers.
We give a q-analogue of Gauss' divisibility theorem