In the present work we prove the following conjecture of Erdos, Roth, Sárközy and T. Sós: Let $f$ be a polynomial of integer coefficients such that 2|f(z) for some integer $z$. Then, for any $k$-colouring of the integers, the equation $x+y=f(z)$ has a solution in which $x$ and $y$ have the same colour. A well-known special case of this conjecture referred to the case f(z)=z2.
ASJC Scopus subject areas
- Theoretical Computer Science
- Statistics and Probability
- Computational Theory and Mathematics
- Applied Mathematics