Integers that are not the sum of positive powers

• Published in 2024
• Added on 2024-06-21

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.

Links

• http://arxiv.org/abs/2404.08193v1
• http://arxiv.org/pdf/2404.08193v1

Other information

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 = {2024-12-07},
	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}
}