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Mock AIME 6 2006-2007 Problems/Problem 14

Revision as of 10:26, 23 November 2023 by Tomasdiaz (talk | contribs) (Created page with "==Problem== A rational <math>\frac{1}{k}</math>, where <math>k</math> is a positive integer, is said to be <math>\textit{n-unsound}</math> if its base <math>N</math> represent...")
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Problem

A rational $\frac{1}{k}$, where $k$ is a positive integer, is said to be $\textit{n-unsound}$ if its base $N$ representation terminates. Let $S_n$ be the set of all $\textit{n-unsound}$ rationals. The sum of all the elements in the union set $S_2\cup S_3\cup\cdots\cup S_{14}$ is $\frac mn$, where $m$ and $n$ are relatively prime positive integers. Find $m+n$.

Solution

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