APPLICATIONS OF THE LEGENDARY SYMBOL
Keywords:
comparison, modulus, residue class, Legendre symbol.Abstract
In studying Legendre 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.
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