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.

X₁^X₂ + X₂^X₃ + X₃^X₁ = X₁X₂X₃ ± 6

Note: X₁X₂X₃ denotes the concatenation of the three digits.

(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