- #1
Tamas
- 2
- 0
Find a perfect power k^m > 1 where k, m, k^m do not contain 2 in their decimal digits, nor do share any decimal digit, no matter if k^m might possibly be expressed in more than one way for some value, e.g. 8^2 = 4^3. I do not know if such an integer exists at all, or how many and how large they are if they do. What did I do to try finding a solution to this problem? I cannot compute or program, so I tried an online big integer calculator with manual input and checking. This was, though methodical, but slow. I got to very large numbers without success, and the more digits appeared, the less likelihood remained for finding a match. Since I am not a mathematician, let alone a number theorist, I cannot prove or disprove the existence of such integer. Finding one can be a proof, but it is beyond my capabilities. Still, this interesting problem fascinates me and I hope others will like it too.