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A quartic polynomial \(f(x)\) with a positive integer leading coefficient is tangent to the line \(y=x+2\) at \(x=\pm k\) for some positive integer \(k>1\). Find the ...

As \(n\) approaches infinity, \(\dbinom{2n}{n}\) is asymptotic to \(k\dfrac{A^n}{n^B}\) for some positive constant \(k.\) Find the value of \(\dfrac{A}{B}.\)

\[x^{1729}\equiv 1\pmod{2017}\]

How many positive integer solutions \(x<2017\) does the congruency above have?

\[\large \int_{-1/\sqrt{3}}^{1/\sqrt{3}} \dfrac{x^2(1-x^2)}{(e^x+1)(1+x^2)^4} \, dx \]

If the above integral is equal to ...

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