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Description: |
Is it possible to color the natural numbers with finitely many colors, so that whenever x and y are of the same color, their sum x+y has a different color? A 1916 theorem of I. Schur tells us that the answer is *no*. In other words, for any finite coloring of N, there exist x and y such that the triple {x,y,x+y} is *monochromatic* (i.e. has all terms have the same color). A similar result holds if one replaces the sum x+y with the product xy, however, it is still unknown whether one can finitely color the natural numbers in a way that no quadruple {x,y,x+y,xy} is monochromatic! In this talk I will present a recent partial solution to this problem, showing that any finite coloring of the natural numbers yields a monochromatic triple {x,x+y,xy}.
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Date: |
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| Start Time: |
15:00 |
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Speaker: |
Joel Moreira (Ohio State Univ., USA)
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Institution: |
Ohio State University
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Place: |
Room 5.5 DMUC
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| Research Groups: |
-Algebra and Combinatorics
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See more:
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<Main>
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