More sum-product type counterexamples: products with shifts and $AA+A$

Oliver Roche-Newton, Carl Schildkraut, Audie Warren

Adapting the construction disproving the sum-product conjecture over $\mathbb{R}$ present in Bloom, Sawin, Schildkraut and Zhelezov, we show the existence of a constant $c>0$ and ar…