Exponential triples (Q554001)
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| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Exponential triples |
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Exponential triples (English)
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29 July 2011
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Summary: 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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ultrafilter techniques
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exponential \(IP\) set
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