Definition
Let n be a non-zero integer, with prime factorization
where u is a unit (i.e., u is 1 or −1), and the pi are primes. Let a be an integer. The Kronecker symbol (a|n) is defined by
For odd pi, the number (a|pi) is simply the usual Legendre symbol. This leaves the case when pi = 2. We define (a|2) by
Since it extends the Jacobi symbol, the quantity (a|u) is simply 1 when u = 1. When u = −1, we define it by
Finally, we put
These extensions suffice to define the Kronecker symbol for all integer values n.
Read more about this topic: Kronecker Symbol
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