2012 USAMO Problems/Problem 1: Difference between revisions
Created page with "==Problem== Find all integers <math>n \ge 3</math> such that among any <math>n</math> positive real numbers <math>a_1</math>, <math>a_2</math>, <math>\dots</math>, <math>a_n</mat..." |
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==See also== | ==See also== | ||
*[[USAMO Problems and Solutions]] | |||
{{USAMO newbox|year=2012|beforetext=|before=First Problem|num-a=2}} | {{USAMO newbox|year=2012|beforetext=|before=First Problem|num-a=2}} | ||
such that among any 
positive real numbers 
, 
, 
, 
with
![\[\max(a_1, a_2, \dots, a_n) \le n \cdot \min(a_1, a_2, \dots, a_n),\]](http://latex.artofproblemsolving.com/c/e/e/ceee7231e7bcd541488519c12e11c9ff7478d0c3.png)
there exist three that are the side lengths of an acute triangle.
