Congruences of Power Sums
Nicholas J. Newsome, Maria S. Nogin, and Adnan H. Sabuwala

TL;DR
This paper extends known congruences of power sums to prime powers and analyzes the periodicity of the sequence of power sums modulo k, providing new insights into their algebraic properties.
Contribution
It generalizes the classical congruence for power sums to prime powers and characterizes the periodicity of the sequence of power sums modulo k.
Findings
Extended congruence to prime power moduli.
Proved periodicity of power sum sequences modulo k.
Determined the explicit period of these sequences.
Abstract
The following congruence for power sums, , is well known and has many applications: where and is prime. We extend this congruence, in particular, to the case when is any power of a prime. We also show that the sequence is periodic and determine its period.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsHistory and Theory of Mathematics · Analytic Number Theory Research · Mathematics and Applications
