The ternary Goldbach problem with prime numbers of a mixed type
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چکیده
منابع مشابه
The ternary Goldbach problem
Leonhard Euler (1707–1783) – one of the greatest mathematicians of the eighteenth century and of all times – often corresponded with a friend of his, Christian Goldbach (1690–1764), an amateur and poly-math who lived and worked in Russia, just like Euler himself. In a letter written in June 1742, Goldbach made a conjecture – that is, an educated guess – on prime numbers: Es scheinet wenigstens,...
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Praeludium We will call prime numbers the integers n ≥ 2 which are divisible only by 1 and themselves. Euclid (fourth century B. C.) first showed that there exist infinitely many prime numbers. His proof is an excellent example of a mathematical argument: if 2, 3, 5, . . . , p were the only prime numbers, we could construct the number 2 · 3 · 5 · · · p + 1, which has the property of leaving the...
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متن کاملThe ternary Goldbach problem with primes in positive density sets
Let P denote the set of all primes. P1, P2, P3 are three subsets of P . Let δ(Pi) (i = 1, 2, 3) denote the lower density of Pi in P , respectively. It is proved that if δ(P1) > 5/8, δ(P2) ≥ 5/8, and δ(P3) ≥ 5/8, then for every sufficiently large odd integer n, there exist pi ∈ Pi such that n = p1 + p2 + p3. The condition is the best possible.
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ژورنال
عنوان ژورنال: Notes on Number Theory and Discrete Mathematics
سال: 2018
ISSN: 1310-5132,2367-8275
DOI: 10.7546/nntdm.2018.24.2.6-20