Dhananjay P. Mehendale. On Goldbach Conjecture

Natural Sciences / Mathematics / Number theory

Submitted on: Jul 24, 2014, 12:41:00

Description: Goldbach conjecture asserts that every even integer greater than 4 is sum of two odd primes. Stated in a letter to Leonard Euler by Christian Goldbach in 1842, this is still an enduring unsolved problem. In this paper we develop a new simple strategy to settle this most easy to state problem which has baffled mathematical community for so long. We show that the existence of two odd primes for every even number greater than 4 to express it as their sum follows from the well known Chinese remainder theorem. We develop a method to actually determine a pair (and subsequently all pairs) of primes for any given even number to express it as their sum. For proof sake we will be using an easy equivalent of Goldbach conjecture. This easy equivalent leads to a congruence system and existence of solution for this congruence system is assured by Chinese remainder theorem. Each such solution actually provides a pair of primes to express given even number as their sum.

The abstract of this article will be published in the July 2014 issue of "Intellectual Archive Bulletin", ISSN 1929-1329.

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