Motivation of Jacobi symbol

Mathematics Asked by athos on December 9, 2020

I fancy the motivation of introducing Legendre symbol is to simplify the quadratic residue check.

But, for Jacobi symbol, even when its value is 1, it doesn’t necessary means that its Legendre Symbol is 1: $$left(frac 2 {15}right)_{Jacobi} = left(frac 2 3right)left(frac 2 5right) =-1*-1 = 1$$
, and 2 is not quadratic residue of 15.

So what is the motivation of introducing Jacobi symbol?

Wiki introduced its usage in Primality_testing , "This is the basis for the probabilistic Solovay–Strassen primality test and refinements such as the Baillie-PSW primality test and the Miller–Rabin primality test." Are there other usages?

Add your own answers!

Related Questions

Ball / Urn question with a twist

1  Asked on December 3, 2021 by user109387


Is an automorphism a function or a group?

2  Asked on December 1, 2021 by josh-charleston


Ask a Question

Get help from others!

© 2022 All rights reserved. Sites we Love: PCI Database, MenuIva, UKBizDB, Menu Kuliner, Sharing RPP