Best equations to analyze using Big O

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Anonymous_001
What would be interesting equations to work with, using Big O?
I'm searching for something that may look simple at first, but can evolve into something more complex!
 
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fresh_42 said:
How about ##SAT \in \mathcal{P}\,##?

You should be far more specific in order to anybody know what you are talking about? Do you want to practice the use of Landau symbols or are you looking for interesting problems in computation science or number theory?

I am looking for interesting problems in number theory!