Séminaire Lotharingien de Combinatoire, B21k (1989).
[Formerly: Publ. I.R.M.A. Strasbourg, 1990, 413/S-21, p. 76-81.]

Hanno Lefmann

Partitionsreguläre Gleichungssysteme

Abstract. 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 partition regular 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.