There are infinitely many Hilbert cubes of dimension 3 in the set of squares

Andrew Bremner, Christian Elsholtz, Maciej Ulas

For an integer tuple $(a_0,a_1,\dots ,a_d)$ with $a_i\ne 0$ for $i=1,\dots ,d$, we define the associated Hilbert cube by \[ H(a_0;a_1,\ldots,a_d) = \left\{ a_0+\sum_{i=1}^d \vareps…