User talk:Eduard Dyachenko

About the combination of: harmonic intervals built on the 'tetrada', the problem 3x+1 and the fundamental constant 4:3
A. The following work DOI 10.5281/zenodo.3630682 proves that the Collatz transformation leads the “length of a number” indicated in the system q = 4∩3  to a unit length.

- The main idea is that reduction of the "length of the number" occurs when converting oddness of the form 4k+1 and preservation of the "length of the number" when converting oddness of the form 4k+3.

- Since the transformation 4k+3 cannot be stored indefinitely, periodically the "length of the number" decreases.

- As a result of consequent iterations the number transforms into the form 2^p/3^q.

B. Simultaneously, during the Collatz transformation of the number (position A), it appears in the system qi = 2∩3.

C. The record of the number in system qi = 2∩3 (B) consists of the sum of elementary numbers in form  {(2^a(ⅈ) -2^b(ⅈ) )/3^ }

D. Example: number 27 = 3/3⋅q^9+2/3⋅q^8+1/3 q^7+0⋅q^6+2/3 q^5+0⋅q^4+1/3 q^3+1/3 q^2+0⋅q^1+1/3 q^0 and its transformation (see table)

E. Find complete prove here (https://zenodo.org/record/4013334#.X1DhOcgzbIU).

- Eduard Dyachenko (talk) 08:59, 27 March 2020 (UTC) E.Dyachenko (dyachenko.eduard@gmail.com)