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Tag: dashed line

14. A recursive property of linear dashed lines with two by two coprime components

14. A recursive property of linear dashed lines with two by two coprime components

Scritto il July 24, 2020November 4, 2020
Pubblicato inDashed line theory
In this post we'll talk about a recursive property, that is true for all linear dashed lines with two by…
Calculation of t_value for dashed lines of arbitrary order

Calculation of t_value for dashed lines of arbitrary order

Scritto il January 11, 2020December 17, 2020
Pubblicato inDashed line theory , Goldbach's conjecture
Prerequisites: Dashed line theory definitions and symbols Computation of a dash value in a linear third order dashed line First…
Factorization dashed lines

Factorization dashed lines

Scritto il January 2, 2020November 28, 2020
Pubblicato inDashed line theory
Prerequisites: Our proof strategies Periodicity and symmetry in linear dashed lines When constructing a linear dashed line, the sequence of…
Study of existence of complementary space pairs based on second order dashed lines

Study of existence of complementary space pairs based on second order dashed lines

Scritto il December 30, 2019December 7, 2020
Pubblicato inDashed line theory , Goldbach's conjecture
Prerequisites: Dashed line theory definitions and symbols Our proof strategies Proof strategy based on dashes Characterization of spaces The purpose…
Calculation of t_space for dashed lines of arbitrary order

Calculation of t_space for dashed lines of arbitrary order

Scritto il December 29, 2019December 17, 2020
Pubblicato inDashed line theory
Prerequisites: Computation of spaces in second order linear dashed lines Inclusion-exclusion principle (preferential) By now, the formula for calculation of…
Characterization of spaces

Characterization of spaces

Scritto il December 29, 2019November 28, 2020
Pubblicato inDashed line theory
Prerequisites: Dashed line theory definitions and symbols Computation of a dash value in a linear third order dashed line Computation…
Upper bound for maximum distance between consecutive spaces

Upper bound for maximum distance between consecutive spaces

Scritto il December 29, 2019December 1, 2020
Pubblicato inDashed line theory , Goldbach's conjecture
Prerequisite: Characterization of spaces General aspects One of the still open problems of dashed line theory is, given a linear…
Our proof strategies: an overview

Our proof strategies: an overview

Scritto il December 18, 2019November 20, 2020
Pubblicato inDashed line theory , Goldbach's conjecture
Prerequisites: Goldbach’s conjecture From prime numbers to dashed lines Periodicity and symmetry in linear dashed lines As already stated, our…
13. Computation of spaces in second order linear dashed lines

13. Computation of spaces in second order linear dashed lines

Scritto il October 28, 2019May 3, 2020
Pubblicato inDashed line theory
In this post we'll see how to obtain a formula for computing the t_space function for second order linear dashed…
12. Computation of a dash value in a linear third order dashed line

12. Computation of a dash value in a linear third order dashed line

Scritto il August 16, 2019May 2, 2020
Pubblicato inDashed line theory
In order to compute the x-th dash value in a third order linear dashed line, we can proceed in a…
11. Computation of a dash value in a linear second order dashed line

11. Computation of a dash value in a linear second order dashed line

Scritto il July 27, 2019May 1, 2020
Pubblicato inDashed line theory
In this post we'll see how it's possible to compute the x-th dash value in a second order linear dashed…
10. Row computation and differences between dash values

10. Row computation and differences between dash values

Scritto il July 13, 2019May 1, 2020
Pubblicato inDashed line theory
It's worth, before passing to the formulas of t_value, pausing for a while and looking closely to the moduli we…
9. Row computation in third order linear dashed lines

9. Row computation in third order linear dashed lines

Scritto il June 23, 2019April 26, 2020
Pubblicato inDashed line theory
For third order linear dashed lines, like second order ones, there exist some particular moduli which, by evaluating proper conditions,…
8. Row computation in second order linear dashed lines

8. Row computation in second order linear dashed lines

Scritto il June 18, 2019April 26, 2020
Pubblicato inDashed line theory
It may sound strange, but it's possible to compute a dash row without having an idea of its value (that…
3. Periodicity and symmetry in linear dashed lines

3. Periodicity and symmetry in linear dashed lines

Scritto il June 14, 2019October 6, 2020
Pubblicato inDashed line theory
In this post we'll talk about two fundamental properties of linear dashed lines: periodicity and symmetry. When we talk about…
7. Downcast characteristic equations of t and t_value for linear dashed lines

7. Downcast characteristic equations of t and t_value for linear dashed lines

Scritto il May 18, 2019April 25, 2020
Pubblicato inDashed line theory
Solving the downcast problem, for linear dashed lines, means finding the solution of particular equations, called "downcast characteristic equations". In…
5. First order linear dashed lines

5. First order linear dashed lines

Scritto il May 16, 2019April 18, 2020
Pubblicato inDashed line theory
We saw that one of the main problems of dashed line theory is computing the t, t_value and t_space functions.…
6. The downcast problem

6. The downcast problem

Scritto il April 21, 2019April 19, 2020
Pubblicato inDashed line theory
The difficulty of computing the t, t_value and t_space functions, increases as the order of the dashed line does. Their…
2. Dashed lines, dashes and spaces: some definitions and simple properties

2. Dashed lines, dashes and spaces: some definitions and simple properties

Scritto il December 21, 2018September 11, 2020
Pubblicato inDashed line theory
In the formal definition of dashed line, a dash is a couple of natural numbers (i, n), where i identifies…
1. From prime numbers to dashed lines

1. From prime numbers to dashed lines

Scritto il December 20, 2018March 29, 2020
Pubblicato inDashed line theory
A dashed line can be represented as a table having a fixed number of rows, and, potentially, infinite columns, numbered…

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  • Home
  • Goldbach’s conjecture
    • Origins of the two Goldbach’s conjectures
    • Some important results
    • Our proof strategies
    • Our readers’ contributions
  • Number theory
    • Foundations of number theory
    • Bertrand’s Postulate
    • Chebyshev’s Theorem (weak version)
    • Chebyshev’s Theorem (strong version)
    • The Prime Number Theorem: the “elementary” proof
    • Complementary material
    • Fun facts
  • Dashed line theory
  • Info
    • About us
    • The project
    • Donations
    • Prizes
  • ItalianoItaliano