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Each natural number is painted either green or yellow but not both. The coloring is called "beautiful" if the sum of any two distinct green numbers is green and the sum of any two distinct of any two distinct yellow numbers is yellow. How many distinct "beautiful" colorings are there?

Guest Nov 14, 2018
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I have to think more about this but I don't believe there are any beautiful colorings.

 

If the operation had been multiplication you could split the evens and odds up but odd plus odd = even.

Rom  Nov 15, 2018

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