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All bases comply (Posted on 2013-06-17) Difficulty: 2 of 5
The sum of the digits of the largest 2-digits square in any base is always equal to its square root.

Prove it.

No Solution Yet Submitted by Ady TZIDON    
Rating: 2.0000 (1 votes)

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Solution Base k (spoiler) Comment 1 of 1
In base k, the smallest 3 digit square = k*k = 100 (base k)

The smallest 2 digit square is therefore (k-1)*(k-1)
 = k*k - 2k + 1 = (k-2)*k + 1

In base k, its digits are (k-2) and 1, and they sum to (k-1), which is its square root


Edited on June 17, 2013, 11:05 am
  Posted by Steve Herman on 2013-06-17 11:05:22

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