_{1}, X

_{2}and X

_{3}represents a nonzero digit of the 3-digit base M positive integer X

_{1}X

_{2}X

_{3}; where X

_{1}, X

_{2}and X

_{3}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.

X

_{1}

^{X2}+ X

_{2}

^{X3}+ X

_{3}

^{X1}= X

_{1}X

_{2}X

_{3}± 6

__Note__: X

_{1}X

_{2}X

_{3}denotes the concatenation of the three digits.