Northeastern WOOTers Mock AIME I Problems/Problem 15

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Problem 15

Find the sum of all integers $n\le96$ such that \[\phi(n)>n-\sqrt{n},\] where $\phi(n)$ denotes the number of integers less than or equal to $n$ that are relatively prime to $n$.



Solution

\begin{claim} $\phi(n)>n-\sqrt{n}$ if and only if $n$ is prime. \end{claim}

Unknown environment 'proof'