Legendre Symbol Calculator

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Posted by Dinesh on

Legendre symbol: For odd primes p and integers a not divisible by p we put (a ÷ p) = 1 or (a ÷ p) = −1 according asais a square modulopor not. The Legendre symbol reveals the parity of a non-zero integer mod p.

Wiki Definition:
In number theory, the Legendre symbol is a multiplicative function with values 1, −1, 0 that is a quadratic character modulo an odd prime number p: its value at a (nonzero) quadratic residue mod p is 1 and at a non-quadratic residue (non-residue) is −1. Its value at zero is 0.

This calculator calculates the legendre symbol using integer, odd primes values.

The following is a table of values of Legendre symbol ( a ÷ p ) with p ≤ 127, a ≤ 30, p odd prime.

a
p
 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30
3 -1 -1 0 -1 -1 0 1 -1 -0 1 -1 0 1 -1 0 -1 -1 0 1 -1 0 1 -1 0 -1 -1 0 1 -1 0
5 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0 1 -1 -1 1 0
7 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1 -1 1 -1 -1 0 1 1
11 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1 1 -1 0 1 -1 1 1 1 -1 -1 -1
13 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1 -1 -1 -1 -1 1 1 -1 1 0 1 -1 1 1
17 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 1 0 1 1 -1 1 -1 -1 -1 1 1 -1 -1 -1 1
19 1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 -1 1 1 -1 0 1 -1 -1 1 1 1 1 -1 1 -1 1
23 1 1 1 1 -1 1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 1 -1 -1 -1 -1 0 1 1 1 1 -1 1 -1
29 1 -1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 1 0 1
31 1 1 -1 1 1 -1 1 1 1 1 -1 -1 -1 1 -1 1 -1 1 1 1 -1 -1 -1 -1 1 -1 -1 1 -1 -1
37 1 -1 1 1 -1 -1 1 -1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 -1 1
41 1 1 -1 1 1 -1 -1 1 1 1 -1 -1 -1 -1 -1 1 -1 1 -1 1 1 -1 1 -1 1 -1 -1 -1 -1 -1
43 1 -1 -1 1 -1 1 -1 -1 1 1 1 -1 1 1 1 1 1 -1 -1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1
47 1 1 1 1 -1 1 1 1 1 -1 -1 1 -1 1 -1 1 1 1 -1 -1 1 -1 -1 1 1 -1 1 1 -1 -1
53 1 -1 -1 1 -1 1 1 -1 1 1 1 -1 1 -1 1 1 1 -1 -1 -1 -1 -1 -1 1 1 -1 -1 1 1 -1
59 1 -1 1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 1 -1 1 1 1 1 -1 -1 1 1 1 1 1 -1
61 1 -1 1 1 1 -1 -1 -1 1 -1 -1 1 1 1 1 1 -1 -1 1 1 -1 1 -1 -1 1 -1 1 -1 -1 -1
67 1 -1 -1 1 -1 1 -1 -1 1 1 -1 -1 -1 1 1 1 1 -1 1 -1 1 1 1 1 1 1 -1 -1 1 -1
71 1 1 1 1 1 1 -1 1 1 1 -1 1 -1 -1 1 1 -1 1 1 1 -1 -1 -1 1 1 -1 1 -1 1 1
73 1 1 1 1 -1 1 -1 1 1 -1 -1 1 -1 -1 -1 1 -1 1 1 -1 -1 -1 1 1 1 -1 1 -1 -1 -1
79 1 1 -1 1 1 -1 -1 1 1 1 1 -1 1 -1 -1 1 -1 1 1 1 1 1 1 -1 1 1 -1 -1 -1 -1
83 1 -1 1 1 -1 -1 1 -1 1 1 1 1 -1 -1 -1 1 1 -1 -1 -1 1 -1 1 -1 1 1 1 1 1 1
89 1 1 -1 1 1 -1 -1 1 1 1 1 -1 -1 -1 -1 1 1 1 -1 1 1 1 -1 -1 1 -1 -1 -1 -1 -1
97 1 1 1 1 -1 1 -1 1 1 -1 1 1 -1 -1 -1 1 -1 1 -1 -1 -1 1 -1 1 1 -1 1 -1 -1 -1
101 1 -1 -1 1 1 1 -1 -1 1 -1 -1 -1 1 1 -1 1 1 -1 1 1 1 1 1 1 1 -1 -1 -1 -1 1
103 1 1 -1 1 -1 -1 1 1 1 -1 -1 -1 1 1 1 1 1 1 1 -1 -1 -1 1 -1 1 1 -1 1 1 1
107 1 -1 1 1 -1 -1 -1 -1 1 1 1 1 1 1 -1 1 -1 -1 1 -1 -1 -1 1 -1 1 -1 1 -1 1 1
109 1 -1 1 1 1 -1 1 -1 1 -1 -1 1 -1 -1 1 1 -1 -1 -1 1 1 1 -1 -1 1 1 1 1 1 -1
113 1 1 -1 1 -1 -1 1 1 1 -1 1 -1 1 1 1 1 -1 1 -1 -1 -1 1 -1 -1 1 1 -1 1 -1 1
127 1 1 -1 1 -1 -1 -1 1 1 -1 1 -1 1 -1 1 1 1 1 1 -1 1 1 -1 -1 1 1 -1 -1 -1 1

Legendre Symbol Calculation

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