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Let n be a positive integer.Prove that the given expression

\({ 3 }^{ { 3 }^{ n } }({ 3 }^{ { 3 }^{ n } }+1)+{ 3 }^{ { 3 }^{ n+1 } }-1\quad\) is not a prime.

Let \(r, s\), and \(t\) be the three roots of the equation \[8x^3 + 1001x + 2008 = 0.\]

Find \[(r + s)^3 + (s + t)^3 + (t + r)^3\]

\[\large\left\lceil\sqrt2\right\rceil\times\left\lceil\sqrt3\right\rceil\times\left\lceil\sqrt4\right\rceil\times\cdots\times\left\lceil\sqrt{99}\right\rceil\]

Find the largest ...

Find the sum of all integers such that \( n^{2} - 18n - 4\) will be a perfect square.

Let the roots of the polynomial \(P(x)=x^3+3x^2+4x-8\) be \(r,s\) and \(t\).

Find the value of \(r^3 + s^3 + t^3\).

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