Past exam of the options II course of the University of Oxford / 2011 / C / C2 / c / i

Here $b$ is odd and nonzero. Choose $k=4|b|-1$. This is a positive odd integer, $k\equiv 3(\mathrm{mod}4)$, and $\gcd (k,b)=1$. By multiplicativity of the Jacobi symbol,The coprimality condition ensures that the squared Jacobi symbol is $1$ rather than $0$.