Geodesic
Partitionsreguläre Gleichungssysteme
Séminaire lotharingien de combinatoire, Tome 21 (1989)

Voir la notice de l'acte provenant de la source Séminaire Lotharingien de Combinatoire website

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. 

@article{SLC_1989_21_a10,
     author = {Hanno Lefmann},
     title = {Partitionsregul\"are {Gleichungssysteme}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {21},
     year = {1989},
     url = {http://geodesic.mathdoc.fr/item/SLC_1989_21_a10/}
}
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AU  - Hanno Lefmann
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JO  - Séminaire lotharingien de combinatoire
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VL  - 21
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SLC_1989_21_a10/
ID  - SLC_1989_21_a10
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%0 Journal Article
%A Hanno Lefmann
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%I mathdoc
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%F SLC_1989_21_a10
Hanno Lefmann. Partitionsreguläre Gleichungssysteme. Séminaire lotharingien de combinatoire, Tome 21 (1989). http://geodesic.mathdoc.fr/item/SLC_1989_21_a10/