ON REDUCIBLE AND PRIMITIVE SUBSETS OF FP , I

摘要

A set A ? Fp is said to be reducible if it can be represented in the form A = B + C with B, C ? Fp, |B| , |C| 2. If there are no sets B, C with these properties then A is said to be primitive. First three criteria are presented for primitivity of subsets of Fp. Then the distance between a given set A ? Fp and the closest primitive set is studied. –Dedicated to the memory of Paul Erd?os on the occasion of the 100th anniversary of his birthday.