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3 colors for naturals, 2000(a + b) = c - All-Russian MO 2001 Regional (R4) 10.3

Source:

September 26, 2024
number theorycombinatoricsColoring

Problem Statement

Describe all the ways to color each natural number as one of three colors so that the following condition is satisfied: if the numbers aa, bb and cc (not necessarily different) satisfy the condition 2000(a+b)=c2000(a + b) = c, then they either all the same color or three different colors
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