Excel in math, science, and engineering

Let \(P\) be an interior point of \(\Delta(ABC)\).Let \(Q\) and \(R\) be the reflections of \(P\) in \(AB\) and \(AC\) respectively. If \(QAR\) is a straight line, find ...

What is the only positive prime number that can be expressed as the difference of the squares of two primes?

\( \large 1 \dbinom{25}{5} +2 \dbinom{24}{5} + 3 \dbinom{23}{5} +\cdots + 21 \dbinom{5}{5} = ? \)

Bonus: Generalize the given expression for an easy summation.

\[\large 2^{\tan(x)} + 3^{\tan(x)} + 6^{\tan(x)} = 1\]

Find the value of \(x\) (\(0^{\circ} \le x \le 180^{\circ}\)) that satisfies the equation above.

Find the sum of all natural numbers \(n\ge 3\) such that it is possible to cut a regular \(n-\)gon into some smaller pieces with regular polygonal shape.

If ...

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