Coloring of positive integers

combinatorics elementary-set-theory coloring ramsey-theory

Solution 1:

I believe, though I am not sure, this is what you are looking for: http://books.google.com/books?id=hUGxm9RdTeUC&pg=PA4&lpg=PA4&dq=schur+coloring+of+positive+integers&source=bl&ots=IrYWq_eBSY&sig=wkWhM0nQfCAbAGPCZFoYDHwRYFE&hl=en&sa=X&ei=sWaTUKGjOITk0QHSq4HoBQ&ved=0CE0Q6AEwBw#v=onepage&q=schur%20coloring%20of%20positive%20integers&f=false

Please correct me if I am wrong. This is not something I am familiar with, but is nonetheless very interesting.

Related

An equivalent condition for strong-mixing
Commuting operators and polar decomposition
Weil conjectures - motivation?
Growth $\beta X\setminus X$ of a Banach space $X$
Prove quotient of factorials is integral
How calculate the De Rham cohomology group of $3$-torus: $T^3$?
Interior Sphere Condition
Function that is discontinuous only for integer fractions
The center of a simply connected semisimple Lie group
Emil Artin's proof for Wedderburn's Little Theorem
Factoring a couple $5$th degree polynomials
Orientation on finite dimensional vector spaces over finite fields.