The Proof of a Conjecture of Additive Number Theory |
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Authors: | Alexandru Gica |
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Affiliation: | Faculty of Mathematics, University of Bucharest, Str. Academiei 14, RO-70109, Bucharest 1, Romaniaf1E-mail: alex@al.math.unibuc.rof1 |
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Abstract: | 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=a2+b, the “length” of b being an even number. |
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