The Proof of a Conjecture of Additive Number Theory Original Research Article

The aim of this paper is to show that for any nset membership, variantN, n>3, there exist a, bset membership, variantN* such that n=a+b, the “lengths” of a and b having the same parity (see the text for the definition of the “length” of a natural number). Also we will show that for any nset membership, variantN, n>2, n≠5, 10, there exist a, bset membership, variantN* such that n=a+b, the “lengths” of a and b having different parities. We will prove also that for any prime p≡7(mod 8) there exist a, bset membership, variantN* such that p=a2+b, the “length” of b being an even number.