(a) If $f$ is a radial function on $\mathbb{R}^{n}$ (i.e. $f(x)=\phi(r)$ with $r=|x|$ for $x \in \mathbb{R}^{n}$ ), and $n>2$, then show that $f$ is harmonic on $\mathbb{R}^{n}-\{0\}$ if and only if

$$\phi(r)=a+b r^{2-n}$$

for $a, b \in \mathbb{R}$.

(b) State the mean value theorem for harmonic functions and prove it for $n>2$.

(c) Generalise the statement and the proof of the mean value theorem to the case of a subharmonic function, i.e. a $C^{2}$ function such that $\Delta u \leqslant 0$.