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Powering up the digits II (Posted on 2009-10-22) Difficulty: 3 of 5
Each of X1, X2 and X3 represents a nonzero digit of the 3-digit base M positive integer X1X2X3; where X1, X2 and X3 are not necessarily distinct.

Determine the respective minimum and maximum positive integer value of M, with M < 100, such that this equation has at least one valid solution.

X1X1 + X2X2 + X3X3 = X1X2X3 - 1

Note: X1X2X3 denotes the concatenation of the three digits.

See The Solution Submitted by K Sengupta    
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No Subject | Comment 1 of 3

Sspreadsheet gave me one solution for bases less than 11

323 base 4

 satisfies the equation  58=59-1


  Posted by Ady TZIDON on 2009-10-22 15:37:45
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