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Powering up the digits IV (Posted on 2011-04-21) 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 possible positive integer values of M, with 7 ≤ M ≤ 206, such that this equation has at least one valid solution.

X1X2 + X2X3 + X3X1 = X1X2X3 ± 6

Note: X1X2X3 denotes the concatenation of the three digits.

No Solution Yet Submitted by K Sengupta    
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re: solution Comment 2 of 2 |
(In reply to solution by Dej Mar)

I believe you misunderstood the question.  let
n1=x1x2x3 and
n2=x1^x2+x2^x3+x3^x1
then we need abs(n2-n1)=6,
your solutions are for abs(n2-n1)<=6.
Taking this into consideration, we arrive at the set of possible m's as {7,8,9,11,14,15,17,23,28,118}


  Posted by Daniel on 2012-12-18 15:49:07
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