SOME OBSERVATIONS AND SPECULATIONS ON PARTITIONS INTO <i>d</i>-TH POWERS
نویسندگان
چکیده
Abstract The aim of this article is to provoke discussion concerning arithmetic properties the function $p_{d}(n)$ counting partitions a positive integer n into d th powers, where $d\geq 2$ . Apart from results asymptotic behaviour , little known. In first part paper, we prove certain congruences involving functions various types powers. second paper experimental and contains questions conjectures sequence $(p_{d}(n))_{n\in \mathbb {N}}$ based on computations for $n\leq 10^5$ $d=2$ 10^{6}$ $d=3, 4, 5$
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ژورنال
عنوان ژورنال: Bulletin of The Australian Mathematical Society
سال: 2021
ISSN: ['0004-9727', '1755-1633']
DOI: https://doi.org/10.1017/s0004972721000034