# Tag Archives: jacobi symbol

## A little intro to the Jacobi symbol: Part 3

This is the final post on the Jacobi symbol. Recall that the Jacobi symbol $(m/n)$ for relatively prime integers $m$ and $n$ is defined to be the sign of the permutation $x\mapsto mx$ on the ring $\Z/n$. In the introductory post we saw this definition, some examples, and basic properties for calculation purposes. In Part […]

## A little intro to the Jacobi symbol: Part 2

In the last post, we examined the Jacobi symbol: for two relatively prime integers $m$ and $n$, we defined the Jacobi symbol $(m/n)$ to be the sign of the permutation $x\mapsto mx$ on the ring $\Z/n$. It turns out that the Jacobi symbol plays a part in the theory of quadratic residues. For a number […]

## A little intro to the Jacobi symbol: Part 1

If $m$ and $n$ are relatively prime integers, the Jacobi symbol $(m/n)$ is defined as the sign of the permutation $x\mapsto mx$ on the set $\Z/n$. Let's give a simple example: $(7/5)$. The permutation on $\{1,2,3,4\}$ is given by $(1 2 4 3) = (1 2)(2 4)(4 3)$ which has an odd number of transpositions. […]