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\[ \Large f(x) = x \log_{\log_{|x^2 - 3 | - 2 } (x^2 - 3|x| + 2) } \left( \dfrac{x^3 - |3x+2|}{x^3 - |3x-2|}\right) \]

If the solution to ...

When 2017 is divided by a 2-digit number, what is the largest possible remainder?

Bonus: Generalize this problem.

\[\large \begin {cases} x^{xyz} =y^2 \\ y^{xyz+1}=z^3 \\ z^{xyz+2}=x^4 \end {cases} \]

Let \(x\), \(y\) and \(z\) be positive integers that satisfy the ...

The remainder when \(x^{1959} - 1\) is divided by \((x^2 + 1)(x^2 + x + 1)\) is of the form \(ax^3 + bx^2 + cx + d\).

FInd ...

\[S= \frac{1^{2}}{10}+\frac{2 \times 1^{2}+2^{2}}{10^{2}}+\frac{3 \times 1^{2}+2 \times 2^{2}+3^{2}}{10^{3}}+\cdots \]

The sum ...

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