On algebraic solutions of algebraic Pfaff equations

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Institute of Mathematics, University of Warsaw, Banacha 2 02-097 Warszawa, Poland

We give a new proof of Jouanolou's theorem about non-existence of algebraic solutions to the system

ẋ = z^{s}, ẏ = x^{s}, ż = y^{s}

. We also present some generalizations of the results of Darboux and Jouanolou about algebraic Pfaff forms with algebraic solutions.

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