= Solution
For fixed particle number, <Bose-Einstein condensation> means that a macroscopic fraction occupies the single-particle <ground state>. As $\mu\uparrow0$, the excited-state population reaches its maximum
$$
N_{\rm ex}=B(k_BT)^3\int_0^\infty\frac{x^2}{e^x-1}\,dx=2B\zeta(3)(k_BT)^3.
$$
At the transition this equals $N$, so
$$
\boxed{T_c=\frac1{k_B}\left(\frac{N}{2B\zeta(3)}\right)^{1/3}\propto N^{1/3}.}
$$
Below $T_c$, the <chemical potential> is approximately zero in the large-$N$ continuum description. Additional particles occupy the <ground state>, giving
$$
\boxed{\frac{N_0}{N}\simeq1-\left(\frac T{T_c}\right)^3,\qquad\gamma=3.}
$$
For finite $N$, the actual <chemical potential> remains slightly negative; the saturation statement is the macroscopic approximation used here.
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