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The ternary Goldbach problem with primes in arithmetic progressions modulus prime numbers
Yafang Kong, Ziyi Song, Lingli Ma, Dengzhe Wang
AIMS Mathematics 2025, 10(12): 30828-30850
Published: 30 December 2025
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In this paper, assuming the Landau's conjecture, we obtained an explicit numerical upper bound for the prime modulus of arithmetic progressions, in which the ternary Goldbach problem is solvable. Our result on the quantitative upper bound improved the previous results.

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