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Additive Number Theory via Automata Theory
Theory of Computing Systems, 2019In the paper under review, the authors study several problems in additive number theory by using automata theory. In particular they use a result due to \textit{V. Bruyère} et al. [Bull. Belg. Math. Soc. - Simon Stevin 1, No. 2, 191--238 (1994; Zbl 0804.11024)] and its implementation in Mousavi's software ``Walnut''.
Aayush Rajasekaran +2 more
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The Mathematical Gazette, 1958
The scope of the additive prime number theory is evident from its name. In this part of the theory of numbers we are concerned with the representation of integers as sums of primes; and here the central problem consists in the proof (or possibly refutation) of a celebrated conjecture made by Goldbach in 1742 to the effect that every even integer ≥4 can
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The scope of the additive prime number theory is evident from its name. In this part of the theory of numbers we are concerned with the representation of integers as sums of primes; and here the central problem consists in the proof (or possibly refutation) of a celebrated conjecture made by Goldbach in 1742 to the effect that every even integer ≥4 can
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On a Problem of Additive Number Theory†
Journal of the London Mathematical Society, 1956Let \(\{a_i\}\) be a non decreasing infinite sequence of non negative integers, \(f(n)\) the number of solutions of \(a_i+a_j = n\) and \(r(n)\) the number of solution of \(a_i+a_j \leq n\). \textit{P. Erdős} and \textit{P. Turán} [J. Lond. Math. Soc. 16, 212--215 (1941; Zbl 0061.07301)] conjectured that \(r(n)-cn = O(1)\) cannot hold.
Erdős, Pál, Fuchs, W. H. J.
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1981
One of the most infamous problems is Goldbach’s conjecture that every even number greater than 4 is expressible as the sum of two odd primes. Richstein has verified it up to 4 · 1014, and on 2003-10-03 I learnt that Oliviera e Silva has extended this to 6 · 1016.
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One of the most infamous problems is Goldbach’s conjecture that every even number greater than 4 is expressible as the sum of two odd primes. Richstein has verified it up to 4 · 1014, and on 2003-10-03 I learnt that Oliviera e Silva has extended this to 6 · 1016.
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Probabilistic number theory in additive arithmetic semigroups II
Mathematische Zeitschrift, 2000zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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