Definition:Biquadratic Residue
Jump to navigation
Jump to search
Definition
Let $p$ be an odd prime.
Let $a \in \Z$ be an integer such that $a \not \equiv 0 \pmod p$.
Then $a$ is a biquadratic residue of $p$ if and only if $x^4 \equiv a \pmod p$ has a solution.
That is, if and only if:
- $\exists x \in \Z: x^4 \equiv a \pmod p$
Also known as
A biquadratic residue is also known as a quartic residue.
Also see
Historical Note
The concept of a biquadratic residue was investigated by Carl Friedrich Gauss in his papers of $1828$ and $1832$.