Given a number of capacitors labelled as C,V. Find the minimum number of capacitors needed to get an arrangement equivalent to C_net, V_net

n in series ; m in parallel
$\mathrm{n}=\frac{{\mathrm{V}}_{\mathrm{net}}}{\mathrm{V}}\Rightarrow {\mathrm{V}}_{\mathrm{net}}=\mathrm{Vn}$
Effective capacitance of chain = C/n
${\mathrm{C}}_{\mathrm{net} }=\mathrm{m}\frac{\mathrm{C}}{\mathrm{n}}\Rightarrow \frac{{\mathrm{C}}_{\mathrm{net}}}{\mathrm{C}}=\frac{\mathrm{m}}{\mathrm{n}}$
Total capacitors $\mathrm{nm}=\frac{{\mathrm{C}}_{\mathrm{net}}}{\mathrm{C}}\times \mathrm{n}\times \mathrm{n}$
$=\frac{{\mathrm{C}}_{\mathrm{net}}}{\mathrm{C}}\times {\left[\frac{{\mathrm{V}}_{\mathrm{net}}}{\mathrm{V}}\right]}^2$