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Find the sum of all \(\theta\) such that \[\sin ^8 {\theta} + \cos ^8 {\theta} = \frac{17}{32} \quad \text{where } 0 \leq \theta \leq \pi. \]

While I was commenting on a posted solution in this problem, when I clicked on preview comment, it directed me to the(comment box) topmost solution in the list and ...

Let \(y = 1 + \frac {a_1}{x- a_1} + \frac {a_2}{(x-a_1)(x-a_2)} + \frac {a_3}{(x-a_1)(x-a_2)(x-a_3)}+ \ldots + \frac {a_n}{(x-a_1)(x-a_2) \ldots (x-a_n)} \)

Prove that:

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How many positive integer values of \(n \leq 10000\) satisfy the following conditions :

\(f_1 (n) = n^2 + 10n + 9 \) is divisible by \(7\).

\(f_2 (n)= n^2 + 14n + 4 \) is ...

I don't know if it is only me, but the box in which I enter the solution is too small and hence I can only view a part of ...

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