# PERIODICITY MODULO m AND DIVISIBILITY PROPERTIES OF THE PARTITION FUNCTION(

```@article{Newman1960PERIODICITYMM,
title={PERIODICITY MODULO m AND DIVISIBILITY PROPERTIES OF THE PARTITION FUNCTION(},
author={Morris Newman},
journal={Transactions of the American Mathematical Society},
year={1960},
volume={97},
pages={225-236}
}```
• M. Newman
• Published 1 February 1960
• Mathematics
• Transactions of the American Mathematical Society
has infinitely many solutions in non-negative integers n. This conjecture seems difficult and I have only scattered results. In ?2 of this paper it will be shown that the conjecture is true for m= 5 and 13 by means of congruences derived from the elliptic modular functions, and similar theorems will be proved; for example that p(5n+4)/5 and p(7n+5)/7 fill all residue classes modulo 5 and 7 respectively, infinitely often. In ?1 it will be shown in an elementary way that the conjecture is also…
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• Mathematics
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• 1969
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• Mathematics
• 2003
Let S denote a subset of the positive integers, and let pS(n) be the associated partition function, that is, pS(n) denotes the number of partitions of the positive integer n into parts taken from S.