On Goldbach's problem
R. Vaughan (1972)
Acta Arithmetica
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R. Vaughan (1972)
Acta Arithmetica
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János Pintz (2012)
Acta Arithmetica
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J. Pintz, I. Z. Ruzsa (2003)
Acta Arithmetica
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M. C. Liu, T. Z. Wang (2002)
Acta Arithmetica
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J. Wu (2008)
Acta Arithmetica
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J. Wu (2004)
Acta Arithmetica
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Hongze Li (2003)
Acta Arithmetica
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M. Z. Garaev (2003)
Acta Arithmetica
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Shaoji Feng, Xiaosheng Wu (2012)
Acta Arithmetica
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Hongze Li (2001)
Acta Arithmetica
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J. Sander (1991)
Acta Arithmetica
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János Pintz (2009)
Journal de Théorie des Nombres de Bordeaux
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At the 1912 Cambridge International Congress Landau listed four basic problems about primes. These problems were characterised in his speech as “unattackable at the present state of science”. The problems were the following :
Alberto Perelli (1996)
Revista Matemática Iberoamericana
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Let N be a large positive real number. It is well known that almost all even integers in the interval [N, 2N] are Goldbach numbers, i.e. a sum of two primes. The same result also holds for short intervals of the form [N, N+H], see Mikawa [4], Perelli-Pintz [7] and Kaczorowski-Perelli-Pintz [3] for the choice of admissible values of H and the size of the exceptional set in several problems in this direction. One may ask if similar results hold for thinner sequences of integers...
Enxun Huang (2023)
Czechoslovak Mathematical Journal
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It is proved that every pair of sufficiently large odd integers can be represented by a pair of equations, each containing two squares of primes, two cubes of primes, two fourth powers of primes and 105 powers of 2.