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\[ \large \Bigg \lfloor \sum_{k=1}^{80} \frac{1}{\sqrt{k}} \Bigg \rfloor = \ ?\]

Notation: \(\lfloor \cdot \rfloor\) denotes the floor function.

If \(a,b,c > 0\) and \(a+b+c=3\), find the minimum value of ...

Find the 1973rd non-perfect square.

Clarification: Non-perfect squares are positive integers which cannot be expressed as \(k^2\), where \(k\) is an integer. For example: 2, 3, 5, 7, 8 ...

What is the largest integer \(n\) such that \(2016^n\) divides \(2016!\, ?\)

Let \(a, b, c\) be distinct positive integers such that \(a+b+c \leq 3000000\). Find the maximum value of \(\text{gcd}(ab+1, bc+1, ca+1)\).

\(\) Notation: ...

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