✦ LIBER ✦

The Proof of a Conjecture of Additive Number Theory

✍ Scribed by Alexandru Gica

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 94 KB
Volume: 94
Category: Article
ISSN: 0022-314X
DOI: 10.1006/jnth.2001.2731

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✦ Synopsis

The aim of this paper is to show that for any n ¥ N, n > 3, there exist a, b ¥ N* 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 n ¥ N, n > 2, n ] 5, 10, there exist a, b ¥ N* 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, b ¥ N* such that p=a 2 +b, the ''length'' of b being an even number.

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