There is another way the Jacobi and Legendre symbols differ.
2.
The Legendre symbol is only defined for odd primes " p ".
3.
If " m " is prime, the Jacobi and Legendre symbols agree.
4.
This law, combined with the properties of the Legendre symbol, means that any Legendre symbol can be calculated.
5.
This law, combined with the properties of the Legendre symbol, means that any Legendre symbol can be calculated.
6.
The classical lemma for the quadratic Legendre symbol is the special case,, } }, if, if.
7.
But we are not supposed to use the Gaussian reciprocity law, only the Legendre symbol and some of its basic properties.
8.
One advantage of this notation over Gauss's is that the Legendre symbol is a function that can be used in formulas.
9.
The Legendre symbol was introduced by Adrien-Marie Legendre in 1798 in the course of his attempts at proving the law of quadratic reciprocity.
10.
The following facts, even the reciprocity laws, are straightforward deductions from the definition of the Jacobi symbol and the corresponding properties of the Legendre symbol.
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