Past exam of the mathematics course of the University of Cambridge / 2015 / ii / Paper 4 / 9H / i

False. The Jacobi symbol $(2/15)=(2/3)(2/5)=(-1)(-1)=1$, yet $2$ is not a quadratic residue modulo three. A solution modulo fifteen would give one modulo three, which is impossible. A positive Jacobi symbol need not indicate a square modulo a composite modulus.