Difference between revisions of "2017 USAMO Problems/Problem 5"
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== Problem == | == Problem == | ||
| + | Let <math>\mathbf{Z}</math> denote the set of all integers. Find all real numbers <math>c > 0</math> such that there exists a labeling of the lattice points <math>( x, y ) \in \mathbf{Z}^2</math> with positive integers for which: only finitely many distinct labels occur, and for each label <math>i</math>, the distance between any two points labeled <math>i</math> is at least <math>c^i</math>. | ||
==Solution 1== | ==Solution 1== | ||
Revision as of 02:31, 3 May 2017
Problem
Let 
denote the set of all integers. Find all real numbers 
such that there exists a labeling of the lattice points 
with positive integers for which: only finitely many distinct labels occur, and for each label 
, the distance between any two points labeled is at least 
.
