## The Arithmetic of Binary Representations of Even Positive Integer 2n and Its Application to the Solution of the Goldbach's Binary Problem

**Authors:** Alexander Fedorov

One of causes why Goldbach's binary problem was
unsolved over a long period is that binary
representations of even integer 2n (BR2n) in the view
of a sum of two odd primes(VSTOP) are considered separately
from other BR2n.
By purpose of this work is research of connections
between different types of BR2n. For realization of this
purpose by author was developed the "Arithmetic of binary
representations of even positive integer 2n" (ABR2n).
In ABR2n are defined four types BR2n.
As shown in ABR2n all types BR2n are connected with
each other by relations which represent distribution of
prime and composite positive integers less than 2n
between them.
On the basis of this relations (axioms ABR2n) are
deduced formulas for computation of the number of BR2n
(NBR2n) for each types.
In ABR2n also is defined and computed Average value
of the number of binary sums are formed from odd prime
and composite positive integers $ < 2n $ (AVNBS). Separately
AVNBS for prime and AVNBS for composite positive integers.
We also deduced formulas for computation of deviation
NBR2n from AVNBS.
It was shown that if $n$ go to infinity then NBR2n go to AVNBS
that permit to apply formulas for AVNBS to computation of
NBR2n.
At the end is produced the proof of the Goldbach's binary
problem with help of ABR2n.
For it apply method of a proof by contradiction
in which we make an assumption that for any 2n not exist
BR2n in the VSTOP then make computations at this conditions then
we come to contradiction. Hence our assumption is false
and forall $2n > 2$ exist BR2n in the VSTOP.

**Comments:** 50 Pages.

**Download:** **PDF**

### Submission history

[v1] 2012-08-31 11:43:43

[v2] 2013-04-20 01:22:22

[v3] 2013-07-15 09:43:49

[v4] 2013-11-16 10:16:33

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