A variance method in combinatorial number theory
Glasgow mathematical journal, Tome 10 (1969) no. 2, pp. 126-129
Voir la notice de l'article provenant de la source Cambridge University Press
Let s = s(a1, a2,...., ar) denote the number of integer solutions of the equationsubject to the conditionsthe ai being given positive integers, and square brackets denoting the integral part. Clearly s (a1,..., ar) is also the number s = s(m) of divisors of which contain exactly λ prime factors counted according to multiplicity, and is therefore, as is proved in [1], the cardinality of the largest possible set of divisors of m, no one of which divides another.
Anderson, Ian. A variance method in combinatorial number theory. Glasgow mathematical journal, Tome 10 (1969) no. 2, pp. 126-129. doi: 10.1017/S0017089500000677
@article{10_1017_S0017089500000677,
author = {Anderson, Ian},
title = {A variance method in combinatorial number theory},
journal = {Glasgow mathematical journal},
pages = {126--129},
year = {1969},
volume = {10},
number = {2},
doi = {10.1017/S0017089500000677},
url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089500000677/}
}
[1] 1.Bruijn, N. G. de, van, C.Tengbergen, E. and Kruyswijk, D., On the set of divisors of a number Nieuw Arch. Wiskunde (2) 23 (1951), 191–193. Google Scholar
[2] 2.Anderson, I., On primitive sequences, J. London Math. Soc. 42 (1967), 137–148. Google Scholar | DOI
[3] 3.Anderson, I., On the divisors of a number, J. London Math. Soc. 43 (1968), 410–418. Google Scholar | DOI
Cité par Sources :