On monochromatic solutions of some nonlinear equations in Z/pZ

Details On monochromatic solutions of some nonlinear equations in Z/pZ On monochromatic solutions of some nonlinear equations in Z/pZ

2009-09-17

arxiv.org/abs/0909.3269v1

Mathematics

Combinatorics

8 pages

Scientific paper

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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