# Legendre Symbol Calculator

Legendre Symbol is a mathematical theoretical function (a/p) with values equivalent to 1, -1 and 0 based on a quadratic character modulo 'p'. Here, let 'p' be an odd prime and 'a' be an arbitrary integer. On a non zero quadratic residue mod 'p' , the value is 1. On a non quadratic residue it is -1 and on zero, it is 0. The symbol is used in law of quadratic reciprocity to simplify notation. Find the legendre symbol with numerator and denominator value.

Legendre Symbol is a mathematical theoretical function (a/p) with values equivalent to 1, -1 and 0 based on a quadratic character modulo 'p'. Here, let 'p' be an odd prime and 'a' be an arbitrary integer. On a non zero quadratic residue mod 'p' , the value is 1. On a non quadratic residue it is -1 and on zero, it is 0. The symbol is used in law of quadratic reciprocity to simplify notation. Find the legendre symbol with numerator and denominator value.

Code to add this calci to your website  #### Rules To Find Legendre Symbol

1. (a/n) = (b/n) if a = b mod n.
2. (1/n) = 1 and (0/n) = 0.
3. (2m/n) = (m/n) if n = ±1 mod 8. Otherwise (2m/n) = -(m/n).
4. (Quadratic reciprocity) If m and n are both odd, then (m/n) = (n/m) unless both m and n are congruent to 3 mod 4, in which case (m/n) = -(n/m).

### Example:

If the numerator is 30 and denominator is 23,

#### 30 / 23

= 7 / 23 (i.e., 30 mod 23)
= -2 / 7 (i.e., both odd reciprocol multiply with -1 and take mod)
= -1 / 7
= -1