Legendre symbol

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Legendre symbol

Legendre Symbol.
Let $p$ be an odd prime. The Legendre symbol $\left(\frac{a}{p}\right)$ or $(a|p)$ is defined as:

\left(\frac{a}{p}\right)=\begin{cases}1&\text{if }a\text{ is a quadratic % residue }\;\;(\mathop{{\rm mod}}p)\\ -1&\text{if }a\text{ is a quadratic nonresidue }\;\;(\mathop{{\rm mod}}p)\\ 0&\text{if }p\text{ divides }a\end{cases}

The Legendre symbol can be computed by means of Euler’s criterion or Gauss’ lemma.

Generalizations of this symbol are the Jacobi Symbol and the Kronecker symbol.

Type of Math Object:

Definition

Major Section:

Reference

Groups audience:

Mathematics Subject Classification

11-00 General reference works (handbooks, dictionaries, bibliographies, etc.)
97U20 Textbooks. Textbook research

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hehe latex2html

Permalink Submitted by drini on Mon, 10/08/2001 - 21:25

did you guys notice that latex2html will render $1$ as a gif, but $0$ as text?

how inconsistent can you be? ;]
f
G -----> H G
p \ /_ ----- ~ f(G)
\ / f ker f
G/ker f

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Re: hehe latex2html

Permalink Submitted by akrowne on Tue, 10/09/2001 - 02:38

thats really interesting. maybe i'll check out the code to see why it does that. we want to minimize the number of image files embedded. hopefully we will heavily hack latex2html for planetmath, as it does a *lot* we don't need.
-apk

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formula

Permalink Submitted by vitriol on Sat, 02/16/2002 - 12:48

You might want to add that (a|p) = a^((p-1)/2) (mod p)

however that works in LaTeX :)

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