Mock AIME 1 2006-2007 Problems/Problem 5

Revision as of 16:27, 17 August 2006 by JBL (talk | contribs)

Let $p$ be a prime and $f(n)$ satisfy $0\le f(n) <p$ for all integers $n$. $\lfloor x\rfloor$ is the greatest integer less than or equal to $x$. If for fixed $n$, there exists an integer $0\le y < p$ such that:


$ny-p\left\lfloor \frac{ny}{p}\right\rfloor=1$


then $f(n)=y$. If there is no such $y$, then $f(n)=0$. If $p=11$, find the sum: $f(1)+f(2)+...+f(p^{2}-1)+f(p^{2})$.

Solution

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