Monochromatic Almost-Pythagorean Quadruples

James Leng, Redmond McNamara, Andreas Mountakis

We prove that for any set $A$ with positive multiplicative upper density, there exist $x$, $y$, $z$ and $w$ in $A$ such that $x^2+y^2{w}^2=z^2$, generalizing a result of Frantzik…