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2017 AIME II Problems/Problem 13

Revision as of 11:38, 23 March 2017 by The turtle (talk | contribs) (Created page with "<math>\textbf{Problem 13}</math> For each integer <math>n\geq3</math>, let <math>f(n)</math> be the number of <math>3</math>-element subsets of the vertices of the regular <ma...")
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$\textbf{Problem 13}$ For each integer $n\geq3$, let $f(n)$ be the number of $3$-element subsets of the vertices of the regular $n$-gon that are the vertices of an isosceles triangle (including equilateral triangles). Find the sum of all values of $n$ such that $f(n+1)=f(n)+78$.

$\textbf{Problem 13 Solution}$ $\boxed{245}$

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