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A short intervals result for linear equations in two prime variables.

M. B. S. Laporta (1997)

Revista Matemática de la Universidad Complutense de Madrid

Given A and B integers relatively prime, we prove that almost all integers n in an interval of the form [N, N+H], where N exp(1/3+e) ≤ H ≤ N can be written as a sum Ap1 + Bp2 = n, with p1 and p2 primes and e an arbitrary positive constant. This generalizes the results of Perelli et al. (1985) established in the classical case A=B=1 (Goldbach's problem).

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