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Let \(f:\mathbb{N}^+ \to \mathbb{Q}^+\) satisfies \(f(1) = 2016\) and \(\displaystyle \sum_{i=1}^n f(i) = n^2 f(n)\) for \(n>1\).

If the value of ...

\[\large \begin{cases} a+b+c=0 \\ a^{3}+b^{3}+c^{3}=3 \\ a^{5}+b^{5}+c^{5}=10 \end{cases} \]

If \(a\), \(b\) and \(c\) are real ...

\[ \large 2x^3 + 3x^2 + 3x + 1 = x^3 + 6x^2 + 12x + 8 \]

Find the number of positive integer solutions that satisfy the equation above.

A positive integer will be called awesome if it has the following properties:

It ranges between \(10000\) and \(100000\), not inclusive. Therefore an awesome integer must contain \(5\) digits.

The ...

\[ \large \left( 1 - \dfrac1{2^2} \right)\left( 1 - \dfrac1{3^2} \right)\left( 1 - \dfrac1{4^2} \right)\cdots \left( 1 - \dfrac1{2014^2} \right) \]

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