Jacobi symbols
Jacobi symbols is the plural of Jacobi symbol.
Meaning of Jacobi symbol
Noun
Jacobi symbol (plural Jacobi symbols)
- A mathematical function of integer a and odd positive integer b, generally written (a/b), based on, for each of the prime factors pᵢ of b, whether a is a quadratic residue or nonresidue modulo pᵢ.
- Although the Jacobi symbol ((1009)/(2307))=1, we still cannot determine whether or not the quadratic congruence 1009=x²(mod 2307) is soluble.
Remark 1.6.10. Jacobi symbols can be used to facilitate the calculation of Legendre symbols.2000, Song Y. Yan, Number Theory for Computing, Springer, 2000, Softcover reprint, page 114
- Although the Jacobi symbol ((1009)/(2307))=1, we still cannot determine whether or not the quadratic congruence 1009=x²(mod 2307) is soluble.
Questions about Jacobi symbols
- What is Jacobi symbols the plural of?
- Jacobi symbols is the plural of Jacobi symbol.
Words near Jacobi symbols in the dictionary
Source and license
Adapted from Wiktionary: Jacobi symbols (page history and authors); Jacobi symbol (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.
Last updated:
Cite this entry: “Jacobi symbols.” Word.ws, https://word.ws/jacobi_symbols. Based on Wiktionary, CC BY-SA 4.0.