Abstract
AbstractThe aim of this article is to provoke discussion concerning arithmetic properties of the function
$p_{d}(n)$
counting partitions of a positive integer n into dth powers, where
$d\geq 2$
. Apart from results concerning the asymptotic behaviour of
$p_{d}(n)$
, little is known. In the first part of the paper, we prove certain congruences involving functions counting various types of partitions into dth powers. The second part of the paper is experimental and contains questions and conjectures concerning the arithmetic behaviour of the sequence
$(p_{d}(n))_{n\in \mathbb {N}}$
, based on computations of
$p_{d}(n)$
for
$n\leq 10^5$
for
$d=2$
and
$n\leq 10^{6}$
for
$d=3, 4, 5$
.
Publisher
Cambridge University Press (CUP)
Cited by
3 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献