On the number of integers in a generalized multiplication table

Details On the number of integers in a generalized multiplication table On the number of integers in a generalized multiplication table

2011-02-16

arxiv.org/abs/1102.3236v1

Mathematics

Number Theory

64 pages

Scientific paper

Motivated by the Erdos multiplication table problem we study the following question: Given numbers N_1,...,N_{k+1}, how many distinct products of the form n_1...n_{k+1} with n_i1. In the present paper we generalize these results by establishing the order of magnitude of A_{k+1}(N_1,...,N_{k+1}) for arbitrary choices of N_1,...,N_{k+1} when k is 2,3,4 or 5. Moreover, we obtain a partial answer to our question when k>5. Lastly, we develop a heuristic argument which explains why the limitation of our method is k=5 in general and we suggest ways of improving the results of this paper.

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