Let AOD(i) be the sum of digits of i divided by the number of digits of i, or the Average Of Digits.
N is the smallest integer > 1 such that the AOD(N^k) is the same for k in {1,2,3,4}
M has the same requirements as N, except AOD(M) must be an integer.
L has the same requirements as M, except that L is the smallest such integer with AOD(L) equal to some integer other than AOD(M).
Find:
1. N, AOD(N)
2. M, AOD(M)
3. L, AOD(L)
(In reply to
re: Misunderstanding of Part 3 by Steven Lord)
There is a 6digit integer, L, such that the average of it's digits is an integer that is not '3'.
The same is true for L^2, L^3, and L^4
(all 4 have the same average digit)

Posted by Larry
on 20200823 15:58:35 