Exponential triples

Details Exponential triples Exponential triples

2011-07-18

arxiv.org/abs/1107.3494v1

Electronic Journal of Combinatorics, 18(1), 2011, P147

Mathematics

Combinatorics

Scientific paper

Using ultrafilter techniques we show that in any partition of $\mathbb{N}$
into 2 cells there is one cell containing infinitely many exponential triples,
i.e. triples of the kind $a,b,a^b$ (with $a,b>1$). Also, we will show that any
multiplicative $IP^*$ set is an "exponential $IP$ set", the analogue of an $IP$
set with respect to exponentiation.

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