English

On monochromatic solutions of some nonlinear equations in Z/pZ

Combinatorics 2009-09-18 v1 Number Theory

Abstract

Consider an arbitrary coloring of integers with finite number of colors. Is it true that there are x, y such that x + y, xy and x have the same color? This is a well-known question of Ramsey theory has not solved yet. In the article we give a positive answer to the last question in the group Z/pZ, where p is a prime number.

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Cite

@article{arxiv.0909.3269,
  title  = {On monochromatic solutions of some nonlinear equations in Z/pZ},
  author = {I. D. Shkredov},
  journal= {arXiv preprint arXiv:0909.3269},
  year   = {2009}
}

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8 pages