ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

3. Number Theory and Arithmetic Algebraic Geometry

1991 MS Classification: 11 Tolev Doytchin, University of Plovdiv, Bulgaria Additive problem with prime numbers of a special type In 1938 Hua–lo–Ken proved that for every sufficiently large integer N, satisfying the congruence condition N ≡ 5(mod 24), the equation

p_{1}^{2} + p_{2}^{2} + p_{3}^{2} + p_{4}^{2} + p_{5}^{2} = N  (1)

has a solution in prime numbers p_{1}, ..., p_{5}. We are able to prove that under the same conditions, imposed on N, the equation (1) has a solution in prime numbers p_{1}, ..., p_{5} such that each of the numbers p_{1} +2, p_{2} +2, p_{3} +2, p_{4} +2 has at most 6 prime factors and p_{5} +2 has at most 7 prime factors.