This paper will examine the type of Ramsey theory concerned with the preservation of solution to specific linear equations under set partition. That is, if a solution to a linear equation exists in the natural numbers, must one also exist within one set of a partition of the natural numbers? To differentiate sets of a partition of the natural numbers from one another, it is convenient to use colors. Then a solution in just one set of a partition of the natural numbers can be referred to as monochromatic solution, or a solution in a single color. [Page 1]
"Real Number Rado Numbers for the Equation ∑_(i=1)^(m-1)▒x_(i+c=x_m ),"
The Journal of Undergraduate Research: Vol. 9
, Article 13.
Available at: http://openprairie.sdstate.edu/jur/vol9/iss1/13