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\[ \bigstar = 1+ \dfrac {e^2}{2!}+ \dfrac {e^3}{3!}+\cdots \]

Find \(\lfloor 1000 \times \bigstar \rfloor\).

\[\large x^n + y^n = z^n\]

All variables in this equation represent positive integers. Moreover, \(n > 1\).

For what integral value(s) of \(n\) does the equation have ...

\[\large \log_{0.75} \log_2 \sqrt[-2]{ \sqrt{0.125}} =\, ? \]

Consider the equation \(a + b + c = 15\).

How many possible combinations can be formed of the values of \( a,b,c\), where \(a,b,c\) belong to non negative integers.

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