We present a short ultrafilter proof of the existence of monochromatic exponential triples {a, b, b^a} in any finite coloring of the natural numbers. We then generalize the construction and prove a new result on the existence of infinite monochromatic exponential patterns.
Monochromatic exponential triples: An ultrafilter proof
Di Nasso, Mauro;Ragosta, Mariaclara
2023-01-01
Abstract
We present a short ultrafilter proof of the existence of monochromatic exponential triples {a, b, b^a} in any finite coloring of the natural numbers. We then generalize the construction and prove a new result on the existence of infinite monochromatic exponential patterns.File in questo prodotto:
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