User:Daniel Geisler

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I am currently working on publishing my research on tetration and the Ackermann function.

For n \ge 10:


{\;^n}2 \equiv 2948736 \; (mod \; 10^7)

{\;^n}3 \equiv 4195387 \; (mod \; 10^7)

{\;^n}4 \equiv 1728896 \; (mod \; 10^7)

{\;^n}5 \equiv 8203125 \; (mod \; 10^7)

{\;^n}6 \equiv 7238656 \; (mod \; 10^7)

{\;^n}7 \equiv 5172343 \; (mod \; 10^7)

{\;^n}8 \equiv 5225856 \; (mod \; 10^7)

{\;^n}9 \equiv 2745289 \; (mod \; 10^7)

{\;^n}11 \equiv 2666611 \; (mod \; 10^7)

{\;^n}12 \equiv 4012416 \; (mod \; 10^7)

{\;^n}13 \equiv 5045053 \; (mod \; 10^7)

{\;^n}14 \equiv 7502336 \; (mod \; 10^7)

{\;^n}15 \equiv 859375 \; (mod \; 10^7)

{\;^n}16 \equiv 415616 \; (mod \; 10^7)

{\;^n}17 \equiv 85777 \; (mod \; 10^7)

{\;^n}18 \equiv 4315776 \; (mod \; 10^7)

{\;^n}19 \equiv 9963179 \; (mod \; 10^7)


For the Ackermann function with n \ge 10 and k \ge 2:

2 \rightarrow n \rightarrow k \equiv 2948736 \; (mod \; 10^7)

3 \rightarrow n \rightarrow k \equiv 4195387 \; (mod \; 10^7)

4 \rightarrow n \rightarrow k \equiv 1728896 \; (mod \; 10^7)

5 \rightarrow n \rightarrow k \equiv 8203125 \; (mod \; 10^7)

6 \rightarrow n \rightarrow k \equiv 7238656 \; (mod \; 10^7)

7 \rightarrow n \rightarrow k \equiv 5172343 \; (mod \; 10^7)

8 \rightarrow n \rightarrow k \equiv 5225856 \; (mod \; 10^7)

9 \rightarrow n \rightarrow k \equiv 2745289 \; (mod \; 10^7)

11 \rightarrow n \rightarrow k \equiv 2666611 \; (mod \; 10^7)

12 \rightarrow n \rightarrow k \equiv 4012416 \; (mod \; 10^7)

13 \rightarrow n \rightarrow k \equiv 5045053 \; (mod \; 10^7)

14 \rightarrow n \rightarrow k \equiv 7502336 \; (mod \; 10^7)

15 \rightarrow n \rightarrow k \equiv 859375 \; (mod \; 10^7)

16 \rightarrow n \rightarrow k \equiv 415616 \; (mod \; 10^7)

17 \rightarrow n \rightarrow k \equiv 85777 \; (mod \; 10^7)

18 \rightarrow n \rightarrow k \equiv 4315776 \; (mod \; 10^7)

19 \rightarrow n \rightarrow k \equiv 9963179 \; (mod \; 10^7)