Problem 389

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Problem 389: (2007 AMC12A, 24)

For each integer $n>1$, let $F(n)$ be the number of solutions to the equation $\sin{x}=\sin{(nx)}$ on the interval $[0,\pi]$. What is $\sum_{n=2}^{2007} F(n)$? $\mathrm{(A)}\ 2014524 \qquad$ $ \mathrm{(B)}\ 2015028 \qquad$ $ \mathrm{(C)}\ 2015033 \qquad$ $ \mathrm{(D)}\ 2016532 \qquad$ $ \mathrm{(E)}\ 2017033$

Solution

Exercise 389: Solution

For each integer $n>1$, let $G(n)$ be the number of solutions to the equation $\cos x=\cos(nx)$ on the interval $[0,\pi]$. What is $\sum_{n=2}^{100}G(n)$?

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