Bilal Khan: On sparse goldbach sets

V sredo, 19. decembra 2007 bo v okviru Seminarja za algebro predaval Professor Bilal Khan z City University of Ney York, ZDA. Naslov predavanja bo On sparse goldbach sets. Abstract:In this paper, we consider sets of natural numbers P subseteq N = {0,1,2, 3,...} which satisfy a slightly modified version of Goldbach Conjecture, namely, that every x in N is expressible as the arithmetic average of two (not necessarily distinct) elements from P. We call such sets ``Goldbach sets'', and demonstrate the using probabilistic techniques, the existence of Goldbach sets with arbitrarily small positive density in the natural numbers. Partial results are given towards constructive descriptions of sparse Goldbach sets, but it remains open whether one can show the existence of density zero sets without presuming the verity of the infamous Goldbach Conjecture.