On the Partition of an Odd Number into Three Primes in a Prescribed Proportion

We prove that, for any partition 1 = a + b + c of unity into three positive summands, each odd number n can be subdivided into three primes n = p a ( n ) + p b ( n ) + p c ( n ) so that the fraction of the first summand will approach a , that of the second, b , and that of the third, c as n → ∞.

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Bibliographic Details
Published in:Mathematical Notes 2019-07, Vol.106 (1-2), p.98-107
Main Author: Sagdeev, A. A.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Partitions (mathematics)
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Summary:We prove that, for any partition 1 = a + b + c of unity into three positive summands, each odd number n can be subdivided into three primes n = p a ( n ) + p b ( n ) + p c ( n ) so that the fraction of the first summand will approach a , that of the second, b , and that of the third, c as n → ∞.
ISSN:0001-4346
1067-9073
1573-8876
DOI:10.1134/S0001434619070101