Displaying similar documents to “Goldbach numbers represented by polynomials.”

The ternary Goldbach problem.

David Rodney (Roger) Heath-Brown (1985)

Revista Matemática Iberoamericana

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The object of this paper is to present new proofs of the classical ternary theorems of additive prime number theory. Of these the best known is Vinogradov's result on the representation of odd numbers as the sums of three primes; other results will be discussed later. Earlier treatments of these problems used the Hardy-Littlewood circle method, and are highly analytical. In contrast, the method we use here is a (technically) elementary deduction from the Siegel-Walfisz Prime Number Theory....

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

M. B. S. Laporta (1997)

Revista Matemática de la Universidad Complutense de Madrid

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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).