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Baja, Zsolt; Dobák, Dániel; Kovács, Benedek; Pach, Péter Pál; Pigler, Donát
Discrete mathematics, 20/May , Volume: 346, Issue: 5Journal Article
In this paper, we study a Ramsey-type problem for equations of the form ax+by=p(z). We show that if certain technical assumptions hold, then any 2-colouring of the positive integers admits infinitely many monochromatic solutions to the equation ax+by=p(z). This entails the 2-Ramseyness of several notable cases such as the equation ax+y=zn for arbitrary a∈Z+ and n≥2, and also of ax+by=aDzD+…+a1z∈Zz such that gcd(a,b)=1, D≥2, a,b,aD>0 and a1≠0.
