Abstract
Perfect polynomials are a natural analogue (in the ring Fp[x]) of multiperfect numbers (in the ring of integers). The latter numbers are classical objects that are poorly understood, since only their definition is simple. We describe, by elementary methods, the most basic objects in the polynomial case of the general problem. We display, for every prime number p ≢ 1 mod 12 (resp. p ≢ 1 mod 24) many new even non-splitting perfect (resp. unitary perfect) polynomials over Fp. Moreover, for any prime number p ≢ 1 mod 24, new bi-unitary perfect polynomials are also given. These examples substantially improve our knowledge about these kinds of polynomials.
Original language | English (US) |
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Pages (from-to) | 47-62 |
Number of pages | 16 |
Journal | Mathematical Reports |
Volume | 25 |
Issue number | 1 |
DOIs | |
State | Published - 2023 |
Keywords
- (bi-unitary) perfect polynomials
- characteristic p
- finite fields
ASJC Scopus subject areas
- Analysis
- Algebra and Number Theory
- Geometry and Topology
- Applied Mathematics