# zbMATH — the first resource for mathematics

On rainbow solutions to an equation with a quadratic term. (English) Zbl 1187.05077
The paper shows that every three-coloration of positive integers (with $$\geq 1/4$$ upper density for all colors) contains a rainbow (three-colored) solution of the equation $$a-b=c^2$$. This bound is shown to be sharp. The paper also studies the possible rainbow solutions of some modular versions of the quadratic equation above.
##### MSC:
 05D10 Ramsey theory
Full Text: