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Rainbow solutions to the Sidon equation |
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| Authors: | Jacob Fox |
| Affiliation: | a Department of Mathematics, Princeton University, Princeton, NJ 08544, USA b Microsoft Research Theory group, One Microsoft Way, Redmond, WA 98052, USA c Department of Mathematics, Baruch College, CUNY, New York, NY 10010, USA |
| Abstract: | We prove that for every 4-coloring of {1,2,…,n}, with each color class having cardinality more than (n+1)/6, there exists a solution of the equation x+y=z+w with x, y, z and w belonging to different color classes. The lower bound on a color class cardinality is tight. |
| Keywords: | Sidon equation Rainbow solution |
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