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A PROOF OF THE GOLDBACH CONJECTURE
SHAN-GUANG TAN
Abstract. The Goldbach conjecture was given a new and equivalent defini-tion and proved in this paper. The main idea of the proof is that if an even number N = 2n greater than 2 can not be expressed as the sum of two primes, a group of linear equations can be formed for a group of primes smaller than the number n, which should be the solutions of the group of linear equations, so when a contradiction between the expectation and the actual results of solutions is obtained, the Goldbach conjecture will be proved. Thus, the proof
is based upon the fundamental theorem of arithmetic and the theory of Linear Algebra. First, by an assumption that an even number greater than 2 can not be expressed as the sum of two primes, a group of linear equations were formed. Then, by investigating solutions to the group of linear equations, reductions to absurdity were derived to prove the assumption false. Hence, the Goldbach conjecture was proved that even numbers greater than 2 can be expressed as the sum of two primes. |
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