How many cubes are there in ZpZSolutionLet pp be a prime An

How many cubes are there in (Z/pZ)*?

Let pp be a prime. An element a(Z/pZ)a(Z/pZ) is called a cube if there exists b(Z/pZ)b(Z/pZ) such that a=b3a=b3. If p2(mod3)p2(mod3),

Let ZpZp be the multiplicative group of the field F. Find the kernel of the squaring homomorphism f:ZpZpf:ZpZp, f(x)=x3f(x)=x3. Use that to find the order of the image f(Zp)f(Zp)