APPLICATIONS OF THE JACOBIC SYMBOL
Keywords:
comparison, modulus, residue class, Legendre symbol, Jacobi symbol.Abstract
In studying Jacobi symbols, we examine quadratic residues and their properties. The Legendre symbol is used to determine the quadratic relationship between two prime numbers. The Jacobi symbol, on the other hand, is a generalization of the Legendre symbol and is defined for any positive odd number. It is computed as the product of the Legendre symbols corresponding to its prime divisors.Legendre and Jacobi symbols are powerful tools for studying the behavior of integers modulo some number. While the Legendre symbol is based on prime numbers, the Jacobi symbol extends to composite numbers, providing a broader framework for number theory.
References
Polvanov, R. R. (2023). HOLDING PROBLEM FOR SECOND-ORDER GRONWALL BOUNDARY CONTROLS. RESEARCH AND EDUCATION, 2(12), 62-67.
Tolibjon o'g, S. G. A. (2022). CHAOS-EVAUSION PROBLEM IN CLOSED SIMPLE GRAPHS FOR MIXED BOUNDARY CONTROLS.
Jumayev M.E., “Practical on Mathematics Teaching Methods-Tashkent.: Teacher, 2004.
Qahramon o‘g, O. K. I., Hasanboy o‘g, J. R. A., & Hasanboy o‘g, X. J. R. (2024). METHODS FOR CALCULATING SOME LIMITS WITH THE HELP OF A DEFINITE INTEGRAL. JOURNAL OF THEORY, MATHEMATICS AND PHYSICS, 3(6), 23-27.
Umirzaqova, Kamola Oripjanovna. "PERIODIC GIBBS MEASURES FOR HARD-CORE MODEL." Scientific Bulletin of Namangan State University 2.3 (2020): 67-73.
A. Sadullayev, Kh. Mansurov and others, Collection of examples and problems from the course of mathematical analysis I, T., Uzbekistan 1993.
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