Séminaire Lotharingien de Combinatoire, B21k (1989).
[Formerly: Publ. I.R.M.A. Strasbourg, 1990, 413/S-21, p.
R. Rado proved that a
system of homogeneous linear equations with integer
coefficients is partition
regular over the positive integers if and only if the coefficient
matrix satisfies something called the "columns condition" over
the rationals. The
question of partition regularity of nonlinear systems remained open
however. For example, P. Erdös and R. Graham asked
whether the equation 1/x+1/y=1/z is
over the positive integers. We answer this question in this paper.
The paper has been finally published under the title
"On partition regular systems of equations" in
J. Combin. Theory Ser. A 58 (1991), 35-53.