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True or False?

If we remove the trailing zeroes of the factorial \(n!,\) where \(n\) is a positive integer such that \(5 \leq n < 10,\) then the last digit ...

The largest known prime number (As of March 2018) is \(p = 2^{77232917} - 1\).

True or false?

a) The diophantine equation \(p = a^2 + b^2\) with ...

\[\large 2018 \exp \left(\int_{0}^{2 \pi} \cot (x + 2018 - 2018i) \, dx \right) =\ ?\]

Notations:

\[\displaystyle \sum_{n = 1}^{\infty} \frac{\sin^{2} (\text{arctan (n)})}{n^2} = \sum_{n =1}^{\infty} \cos^2 (\text{arctan (n)})=?\] Find a beatiful closed formula for the above ...

How many matrices \(A\) of order 2 over the domain of Gaussian integers (\(\mathbb{Z}[i]\)) satisfy ...

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