No CrossRef data available.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
Published online by Cambridge University Press: 03 November 2016
The congruence x2 ≡ a (mod p), where p is an odd prime and a is any number not divisible by p, sometimes has a solution, but sometimes it has not. Gauss’s symbol (a/p), also known as Legendre’s symbol, is defined as (a/p) = l if there exists at least one x as a solution to this congruence and (a/p) = − l if no such solution exists.
The “Law of Reciprocity”, the famous theorem by Gauss, then states that, if p and q are odd primes,
where 