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- == Legendre Symbol == The symbol <math>\left(\frac{a}{p}\right)</math> is called the [[Legendre symbol]].5 KB (778 words) - 12:10, 29 November 2017
- '''Legendre symbol''': for <math>a \in \mathbb{Z}</math> and [[odd integer | odd]] <math>p \in Then the '''Jacobi symbol''' for <math>a \in \mathbb{Z}</math> and odd <math>n= \prod p_i^{\nu_i}</ma8 KB (1,401 words) - 12:11, 17 June 2008
- ..., and let <math>a</math> be any integer. Then we can define the [[Legendre symbol]] This theorem can help us evaluate Legendre symbols, since the following laws also apply:7 KB (1,182 words) - 15:46, 28 April 2016
- (The symbol <math>[x]</math> denotes the greatest integer not exceeding <math>x</math>. ...th> is the number of 1's in the binary representation of <math>n</math>. [[Legendre's Formula]] states that <math>n-S=\sum_{k=0}^{x} \bigg[\frac{n}{2^{k + 1}}\3 KB (427 words) - 11:49, 5 December 2023
- where <math>\left(\frac{p}{q}\right)</math> is the [[Legendre symbol]], equal to 1 if <math>p</math> is a [[quadratic residue]] modulo <math>q</10 KB (1,646 words) - 14:04, 28 May 2020
- ...(\frac{q}{p}\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}</math>. The Legendre symbol <math>\left(\frac{3}{11}\right)=(-1)\left(\frac{11}{3}\right)=(-1)\left(\fr ...so 3 is a quadratic residue mod 11. For quadratic residues, their Legendre symbol which we know is the answer from Solution 2 is <math>\boxed{\textbf{(E)}\ 13 KB (436 words) - 18:52, 30 July 2024