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In Triangle \(ABC\), \(AD\) is the angle bisector at \(A\). If \( \angle ABD = 30 ^ \circ, \angle DBC = 1 ^ \circ, \angle ACD = 89 ^ \circ \), what is the measure of ...

Find the set of all integers \(n\) such that the number \(n^3 - 9n + 27\) is divisible by 81.

True or False?

If \(a,b\) and \(c\) are roots to the equation \(x^3+x^2 + x=1\), and let \(S_n = a^n + b^n + c^n\), then there ...

\[\large{x^2-6829y^2=1}\]

Find the pair of positive integers \((x, y)\) satisfying the equation above, such that \(x+y\) is minimized. Enter your answer as ...

Find the smallest positive integer \(x\) such that

\[ \large \frac{2x^2+5x+3}{3} \]

is a perfect square.

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