10/24/2021, 12:49 PM
Hi Lunik, welcome to the Tetration forum. I hope you'll find this an inspiring place to share ideas and learn new things.
I have just skimmed thru your paper and atm I can only be in accord with JmsNxn. It is good to chose some particular cases but in the case of number theoretic/\(\mathbb Z/n\mathbb Z\) things I nice rule of thumb would be that of playing around with special cases involving prime numbers properties.
Said that, on first sight, the question of doing tetration (higher hyperoperations) \({\rm mod}\, k\) seems to be related to some recent posts I saw on MSE. I usually take the internal definition route, the synthetic one, when I consider Hyperoperations over finite sets, eg. the \(\mathbb Z/n\mathbb Z\)'s arithmetic, and modding out is more an external approach, i.e. you start from hyperoperations in \(\mathbb Z\) and then you mod out/quotient and study the reminders.
Ps. felice di vedere un'altra persona dall'Italia oltre a me hahah! benvenuto
I have just skimmed thru your paper and atm I can only be in accord with JmsNxn. It is good to chose some particular cases but in the case of number theoretic/\(\mathbb Z/n\mathbb Z\) things I nice rule of thumb would be that of playing around with special cases involving prime numbers properties.
Said that, on first sight, the question of doing tetration (higher hyperoperations) \({\rm mod}\, k\) seems to be related to some recent posts I saw on MSE. I usually take the internal definition route, the synthetic one, when I consider Hyperoperations over finite sets, eg. the \(\mathbb Z/n\mathbb Z\)'s arithmetic, and modding out is more an external approach, i.e. you start from hyperoperations in \(\mathbb Z\) and then you mod out/quotient and study the reminders.
Ps. felice di vedere un'altra persona dall'Italia oltre a me hahah! benvenuto
Mother Law \(\sigma^+\circ 0=\sigma \circ \sigma^+ \)
\({\rm Grp}_{\rm pt} ({\rm RK}J,G)\cong \mathbb N{\rm Set}_{\rm pt} (J, \Sigma^G)\)