Denote "sod(x)" as sum of the digits of x. Examples: sod(49) = 4 + 9 = 13; sod(123) = 1 + 2 + 3 = 6.
Find sod(sod(sod(4444^4444))).
As 4444
4444 can be rewritten as (7 + 9*493)
(4 + 6*740), the two values 7 (as b, the root base) and 4 (as p, the root power) can be cross-referenced with the following cyclic-power digital root function table, following, to show that the application of the digital root function, S[4444
4444], yields 7.
b p=2 p=3 p=4 p=5 p=6 p=7
1: 1 1 1 1 1 1
2: 4 8 7 5 1 2
3: 9 9 9 9 9 9
4: 7 1 4 7 1 4
5: 7 8 4 2 1 5
6: 9 9 9 9 9 9
7: 4 1 7 4 1 7
8: 1 8 1 8 1 8
9: 9 9 9 9 9 9
In this case, sod(4444
4444) = 72601. Thus, sod(sod(4444
4444)) = 7+2+6+0+1 = 16, and, sod(sod(sod(4444
4444))) = 1+6 = 7, which equals and confirms the result of S[4444
4444].
Edited on July 9, 2008, 9:37 pm
|
Posted by Dej Mar
on 2008-07-09 21:27:18 |