2013 Mock AIME I Problems/Problem 7

Problem

Let $S$ be the set of all $7$ th primitive roots of unity with imaginary part greater than $0$ . Let $T$ be the set of all $9$ th primitive roots of unity with imaginary part greater than $0$ . (A primitive $n$ th root of unity is a $n$ th root of unity that is not a $k$ th root of unity for any $1 \le k < n$ .)Let $C=\sum_{s\in S}\sum_{t\in T}(s+t)$ . The absolute value of the real part of $C$ can be expressed in the form $\frac{m}{n}$ where $m$ and $n$ are relatively prime numbers. Find $m+n$ .

Solution

$\boxed{005}$ .

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2013 Mock AIME I Problems/Problem 7

Problem

Solution

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