A generalization of a theorem of Erdös on asymptotic basis of order 2
Journal de théorie des nombres de Bordeaux, Volume 6 (1994) no. 1, p. 9-19

Let 𝒯 be a system of disjoint subsets of * . In this paper we examine the existence of an increasing sequence of natural numbers, A, that is an asymptotic basis of all infinite elements T j of 𝒯 simultaneously, satisfying certain conditions on the rate of growth of the number of representations 𝑟 𝑛 (𝐴);𝑟 𝑛 (𝐴):=(𝑎 𝑖 ,𝑎 𝑗 ):𝑎 𝑖 <𝑎 𝑗 ;𝑎 𝑖 ,𝑎 𝑗 𝐴;𝑛=𝑎 𝑖 +𝑎 𝑗 , for all sufficiently large nT j and j * A theorem of P. Erdös is generalized.

@article{JTNB_1994__6_1_9_0,
     author = {Helm, Martin},
     title = {A generalization of a theorem of Erd\"os on asymptotic basis of order $2$},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {6},
     number = {1},
     year = {1994},
     pages = {9-19},
     zbl = {0812.11011},
     mrnumber = {1305285},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_1994__6_1_9_0}
}
Helm, Martin. A generalization of a theorem of Erdös on asymptotic basis of order $2$. Journal de théorie des nombres de Bordeaux, Volume 6 (1994) no. 1, pp. 9-19. http://www.numdam.org/item/JTNB_1994__6_1_9_0/

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