The Quadratic and Cubic Characters of 2
Abstract
SummaryThe solvability of the cubic congruence x3≡2 (modp) is referred to as the cubic character of 2. In evaluating the cubic character of 2, we introduce the Eisenstein integers, Gauss and Jacobi sums, and the law of cubic reciprocity. We motivate this proof by giving ample historical information surrounding the early development of higher reciprocity laws as well as Gauss' proof of the solvability of the quadratic congruence x2≡2 (modp); conventionally the quadratic character of 2. We simultaneously outline other relevant contributions by Fermat, Euler, Legendre, Jacobi, and Eisenstein.
Fields of Study & Subjects
Advanced Mathematical Identities
History and Theory of Mathematics
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- Mathematics Magazine
- Publisher
- Informa UK Limited
- Pages
- 1–18
- Publication date
- 30 January 2026
- Language
- EN