\b[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.

Solution

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

 Solution (source code)