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A digital root-perfect power problem (Posted on 2008-07-01) Difficulty: 4 of 5
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)

Comments: ( Back to comment list | You must be logged in to post comments.)
Answer | Comment 6 of 7 |
The required smallest value of a is 78125
  Posted by K Sengupta on 2008-12-28 16:22:36
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