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.