Difference between revisions of "G285 2021 MC-IME II"
Geometry285 (talk | contribs) (Created page with "==Problem 1== Let <math>20</math> points lie in the interior of the circumcircle of regular decagon <math>ABCDEFGHIJ</math>. If each point is connected to the second farthest...") |
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==Problem 2== | ==Problem 2== | ||
| + | Suppose <math>\phi(n)</math> denote the number of integer <math>k</math> where <math>1 \le k < n</math> such that <math>\gcd(k,n)=1</math>. If <cmath>\sum_{p=1}^{n} \frac{1}{2^p \phi(p)}</cmath> can be represented as <math>\phi(n) \cdot l</math> for some constant <math>l</math>, find <math>l \mod 1000</math> | ||
Latest revision as of 19:58, 4 July 2021
Problem 1
Let 
points lie in the interior of the circumcircle of regular decagon 
. If each point is connected to the second farthest point away from itself by a line, find the maximum number of regions created by the intersections of lines.
Problem 2
Suppose 
denote the number of integer 
where 
such that 
. If ![\[\sum_{p=1}^{n} \frac{1}{2^p \phi(p)}\]](http://latex.artofproblemsolving.com/9/7/4/9749517444970ddc58003f917713d17b5f8873d8.png)
can be represented as 
for some constant 
, find 
