noun
Meaning 1
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.
Definition source: English Wiktionary via Wiktextract
Topics: mathematics, number-theory, sciences
Examples
- 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. Remark 1.6.10. Jacobi symbols can be used to facilitate the calculation of Legendre symbols.
- 2014, Ibrahim Elashry, Yi Mu, Willy Susilo, Jhanwar-Barua's Identity-Based Encryption Revisited, Man Ho Au, Barbara Carminati, C.-C. Jay Kuo (editors), Network and System Security: 8th International Conference, Springer, LNCS 8792, page 279, From the above equations, guessing the Jacobi symbol ((2y_is_j_1s_j_2+2)/N) from ((2y_j_1s_j_1+2)/N) and ((2y_j_2s_j_2+2)/N) is as hard as guessing them from independent Jacobi symbols.
Meaning relationships
Synonyms: none provided
Antonyms: none provided