# Integers that are not the sum of positive powers

- Published in 2024
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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} }