Interesting Esoterica

Integers that are not the sum of positive powers

Article by Brennan Benfield and Oliver Lippard
  • Published in 2024
  • Added on
Exactly which positive integers cannot be expressed as the sum of \(j\) positive \(k\)-th powers? This paper utilizes theoretical and computational techniques to answer this question for \(k\leq9\). Results from Waring's problem are used throughout to catalogue the sets of such integers. These sets are then considered in a general setting, and several curious properties are established.

Comment

1072 is the sum of 2, 3, 4, 5, 6, 7 and 8 positive cubes.

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Other information

key
Integersthatarenotthesumofpositivepowers
type
article
date_added
2024-06-21
date_published
2024-07-11

BibTeX entry

@article{Integersthatarenotthesumofpositivepowers,
	key = {Integersthatarenotthesumofpositivepowers},
	type = {article},
	title = {Integers that are not the sum of positive powers},
	author = {Brennan Benfield and Oliver Lippard},
	abstract = {Exactly which positive integers cannot be expressed as the sum of \(j\)
positive \(k\)-th powers? This paper utilizes theoretical and computational
techniques to answer this question for \(k\leq9\). Results from Waring's problem
are used throughout to catalogue the sets of such integers. These sets are then
considered in a general setting, and several curious properties are
established.},
	comment = {1072 is the sum of 2, 3, 4, 5, 6, 7 and 8 positive cubes.},
	date_added = {2024-06-21},
	date_published = {2024-07-11},
	urls = {http://arxiv.org/abs/2404.08193v1,http://arxiv.org/pdf/2404.08193v1},
	collections = {easily-explained,fun-maths-facts,integerology},
	url = {http://arxiv.org/abs/2404.08193v1 http://arxiv.org/pdf/2404.08193v1},
	urldate = {2024-06-21},
	year = 2024,
	archivePrefix = {arXiv},
	eprint = {2404.08193},
	primaryClass = {math.NT}
}