If the nonnegative integers are colored with a finite number of colors, does there
necessarily exist an infinite monochromatic arithmetic sequence?
progresie aritmetica monocromatica
progresie aritmetica monocromatica
Liceul Teoretic Cobani
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gigelmarga
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- Membru din: Vin Dec 05, 2014 12:26 am
Re: progresie aritmetica monocromatica
Obviously, not. Two colors suffice to provide a counterexample:ghenghea1 scrie:If the nonnegative integers are colored with a finite number of colors, does there
necessarily exist an infinite monochromatic arithmetic sequence?
Color 1: {1},{4,5,6},{11,12,13,14,15},...
Color 2: {2,3},{7,8,9,10},{16,17,18,19,20,21},...