Kronecker Symbol Calculator
Calculate the Kronecker symbol (a|n), extending the Jacobi symbol to all integers.
Enter Values
Definition
The Kronecker symbol extends the Jacobi symbol:
- (a|0) = 1 if |a| = 1, else 0
- (a|-1) = -1 if a < 0, else 1
- (a|2) depends on a mod 8
(a|2) Values
(a|2) = 0 if a is even
(a|2) = 1 if a ≡ ±1 (mod 8)
(a|2) = -1 if a ≡ ±3 (mod 8)
Kronecker Symbol
(5|21) = 1
a
5
n
21
Result
1
Calculation Steps
Reduce a mod n: a = 5
Swap: now (1/5)
Final result
Result: 1
Applications
- Quadratic forms
- Class field theory
- Quadratic number fields
- Primality testing
💡
Help us improve!
How would you rate the Kronecker Symbol Calculator?
Editorial Note
MyCalcBuddy Editorial Team
This page is maintained as an educational calculator reference.
📚
Formula Source: Handbook of Mathematical Functions
by Abramowitz & Stegun
🔄Last reviewed: May 2026
✓Formula checks are based on standard references and internal QA review.