Geodesic
Exponential triples
The electronic journal of combinatorics, Tome 18 (2011) no. 1
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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.
DOI : 10.37236/634
Classification : 05A18
Mots-clés : ultrafilter techniques, exponential \(IP\) set 
@article{10_37236_634,
     author = {Alessandro Sisto},
     title = {Exponential triples},
     journal = {The electronic journal of combinatorics},
     year = {2011},
     volume = {18},
     number = {1},
     doi = {10.37236/634},
     zbl = {1227.05065},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/634/}
}
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Alessandro Sisto. Exponential triples. The electronic journal of combinatorics, Tome 18 (2011) no. 1. doi: 10.37236/634

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