Let be a system of disjoint subsets of . In this paper we examine the existence of an increasing sequence of natural numbers, , that is an asymptotic basis of all infinite elements of simultaneously, satisfying certain conditions on the rate of growth of the number of representations , for all sufficiently large and 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}, pages = {9--19}, publisher = {Universit\'e Bordeaux I}, volume = {6}, number = {1}, year = {1994}, zbl = {0812.11011}, mrnumber = {1305285}, language = {en}, url = {http://www.numdam.org/item/JTNB_1994__6_1_9_0/} }
TY - JOUR AU - Helm, Martin TI - A generalization of a theorem of Erdös on asymptotic basis of order $2$ JO - Journal de Théorie des Nombres de Bordeaux PY - 1994 DA - 1994/// SP - 9 EP - 19 VL - 6 IS - 1 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_1994__6_1_9_0/ UR - https://zbmath.org/?q=an%3A0812.11011 UR - https://www.ams.org/mathscinet-getitem?mr=1305285 LA - en ID - JTNB_1994__6_1_9_0 ER -
Helm, Martin. A generalization of a theorem of Erdös on asymptotic basis of order $2$. Journal de Théorie des Nombres de Bordeaux, Tome 6 (1994) no. 1, pp. 9-19. http://www.numdam.org/item/JTNB_1994__6_1_9_0/
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