Abstract
Let A = {а 1 < a 2 < ...} be a set of positive integers and A(x) its counting function. Let us denote the number of partitions of n with parts in A by p( A , n). Improving on two preceding papers jointly written with I.Z. Ruzsa and A. Sárközy (J. Number Theory, 1998) and with A. Sárközy (Millennial Conference on Number Theory, May 2000, Urbana, Illinois, U.S.A.), it is shown that there exists a set A satisfying A(x) > c xlog log x/ (log x) 1/3 , c<0, such that, for n large enough, p( A ; n) isalways even.
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Nicolas, JL. On the parity of generalized partition functions II. Periodica Mathematica Hungarica 43, 177–189 (2002). https://doi.org/10.1023/A:1015298018722
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DOI: https://doi.org/10.1023/A:1015298018722