A mean value theorem on the binary Goldbach problem and its application |
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Authors: | Xianmeng Meng |
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Institution: | (1) Shandong Finance Institute, Jinan, P.R. China |
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Abstract: | We study the binary Goldbach problem with one prime number in a given residue class, and obtain a mean value theorem. As an
application, we prove that for almost all sufficiently large even integers n satisfying n ≢ 2(mod 6), the equation p
1 + p
2 = n is solvable in prime variables p
1, p
2 such that p
1 + 2 = P
3, and for every sufficiently large odd integer
satisfying
≢ 1(mod 6), the equation p
1 + p
2 + p
3 =
is solvable in prime variables p
1, p
2, p
3 such that p
1 + 2 = P
2, p
2 + 2 = P
3. Here P
k
denotes any integer with no more than k prime factors, counted according to multiplicity. |
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Keywords: | 2000 Mathematics Subject Classification: 11P32 11N36 |
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