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 A digital root-perfect power problem (Posted on 2008-07-01)
Let S[x] be the digital root function (also known as the repeated digital sum function), where one adds the digits of positive integer x, then adds the digits of the sum until obtaining a single-digit number. (For example, S[975] = 3 because 9 + 7 + 5 = 21 and 2 + 1 = 3).

Given S[aa] = 2, what is the smallest positive integer that a can be such that a is a perfect power?

Note: a is a perfect power if there exist natural numbers m > 1, and k > 1 such that mk = a.

 See The Solution Submitted by Dej Mar Rating: 4.0000 (2 votes)

 Subject Author Date digit counts Daniel 2008-12-29 06:55:56 Answer K Sengupta 2008-12-28 16:22:36 re(2): Extra Credit (spoiler) Steve Herman 2008-07-14 10:33:59 re: Extra Credit (spoiler) Dej Mar 2008-07-10 17:47:35 Extra Credit (spoiler) Steve Herman 2008-07-10 11:35:28 Nailed it, I hope (spoiler) Steve Herman 2008-07-01 20:03:23 Missed it by that much (spoiler) Steve Herman 2008-07-01 19:48:23

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