MathDB
2009 integers around a circle, weird mean Puerto Rico Ibero IMO TST 2009.5

Source:

September 16, 2021
algebranumber theory

Problem Statement

The weird mean of two numbers a a and b b is defined as 2a2+3b25 \sqrt {\frac {2a^2 + 3b^2}{5}}. 2009 2009 positive integers are placed around a circle such that each number is equal to the the weird mean of the two numbers beside it. Show that these 2009 2009 numbers must be equal.
Back to ProblemsView on AoPS