Difference between revisions of "2000 AIME II Problems/Problem 1"

Revision as of 19:21, 11 November 2007

The number

$\frac 2{\log_4{2000^6}} + \frac 3{\log_5{2000^6}}$

can be written as $\frac mn$ where $m$ and $n$ are relatively prime positive integers. Find $m + n$ .

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 == Problem ==
-Find the least positive integer <math>n</math> such that no matter how <math>10^{n}</math> is expressed as the product of any two positive integers, at least one of these two integers contains the digit <math>0</math>.
+The number
+<center><math>\frac 2{\log_4{2000^6}} + \frac 3{\log_5{2000^6}}</math></center>
+can be written as <math>\frac mn</math> where <math>m</math> and <math>n</math> are relatively prime positive integers.  Find <math>m + n</math>.
 == Solution ==

2000 AIME II (Problems • Answer Key • Resources)
Preceded by First Question	Followed by Problem 2
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All AIME Problems and Solutions