# Unity Sum

**Number Theory**Level 5

\[\large \displaystyle 72^3\sum _{m=1}^{72}\sum _{a\ge 1}^{ }\sum _{t\ge 1}^{ }\sum _{h\ge 1}^{ }\frac{\omega^{math}}{(ath)^2}=\frac{A\pi ^B}{C}\]

The equation above holds true where \(\omega=e^{2i \pi/72}\). Find the value of \(A+B+C\)

**Bonus**: Generalise for

\[\large k^s\sum _{b=1}^k\sum _{a_1\ge 1}^{ }\sum _{a_2\ge 1}^{ }\cdots \sum _{a_n\ge 1}^{ }\frac{w^{ba_1a_2\cdots a_n}}{\left(a_1a_2...a_n\right)^s} \; , \]

where \(w=e^{2i \pi/k} \).