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On additive problems with prime numbers of special type

Meng X., Wang M.

Demonstratio Mathematica

2007

Vol. 40, nr 2

271-287

Let Pk denote any integer with no more than k prime factors, counted according to multiplicity. It is proved that for almost all sufficiently large integers n, satisfying n is identical with 0 or 1 (mod 3), the equation n = p1+p2/2 +p2/3 has a solution in primes p1, p2, p3 such that p1+2 = P6, p2+2 = P5, p3+2 = P5. It is also proved that for every suffciently large integer M is identical with 0 or 2 (mod 3), the equation M = p1+p2/2+p2/3+p2/4+p2/5 has a solution in primes p1, ź ź ź , p5 such that p1+2 = P6, p2+2 = P5, p3+2 = P5, p4+2 = P2, p5+2 = P'/2.