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- Apr 16th 2008, 12:35 AMmilfnerJacobi Symbol
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- Apr 16th 2008, 07:00 AMThePerfectHacker
- Apr 21st 2008, 07:31 PMmilfner
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- Apr 21st 2008, 07:34 PMThePerfectHacker
- Apr 22nd 2008, 06:08 PMmilfner
All of them (Headbang)

- Apr 22nd 2008, 07:13 PMThePerfectHacker
The Jabobi symbol is a generalization of the Legendre symbol. Given two integers $\displaystyle a,b$ where $\displaystyle b>1$ and odd. Define $\displaystyle (a/b) = (a/p_1)...(a/p_m)$ where $\displaystyle b=p_1...p_m$ is a factorization of not necessarily distinct primes (here the RHS is the regular Legendre symbol).

Here are some simple properties.

- $\displaystyle (a_1/b) = (a_2/b)$ if $\displaystyle a_1\equiv a_2(\bmod b)$
- $\displaystyle (2/b) = (-1)^{(b^2-1)/8}$
- $\displaystyle (a_1a_2/b) = (a_1/b)(a_2/b)$
- $\displaystyle (a/b)(b/a) = (-1)^{(a-1)/2\cdot (b-1)/2}$ where $\displaystyle a$ is odd and > 1

All of these were used. Figure out which ones. - May 1st 2008, 07:04 PMmilfner
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