# 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 $$w=e^{2i \pi/k}$$.

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