ON GOLDBACH ’S CONJECTURE IN ARITHMETIC PROGRESSIONS
نویسندگان
چکیده
منابع مشابه
On the Goldbach Conjecture in Arithmetic Progressions
It is proved that for a given integer N and for all but (log N)B prime numbers k ≤ N5/48−ε the following is true: For any positive integers bi, i ∈ {1, 2, 3}, (bi, k) = 1 that satisfy N ≡ b1 + b2 + b3 (mod k), N can be written as N = p1+p2+p3, where the pi, i ∈ {1, 2, 3} are prime numbers that satisfy pi ≡ bi (mod k).
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We show that for every fixed A > 0 and θ > 0 there is a θ = θ(A, θ) > 0 with the following property. Let n be odd and sufficiently large, and let Q1 = Q2 := n 1/2(log n)−θ and Q3 := (log n) θ. Then for all q3 ≤ Q3, all reduced residues a3 mod q3, almost all q2 ≤ Q2, all admissible residues a2 mod q2, almost all q1 ≤ Q1 and all admissible residues a1 mod q1, there exists a representation n = p1+...
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ژورنال
عنوان ژورنال: Studia Scientiarum Mathematicarum Hungarica
سال: 2001
ISSN: 0081-6906,1588-2896
DOI: 10.1556/sscmath.37.2001.1-2.1