_{1}and X

_{2}represents a nonzero digit of the 2-digit base M positive integer X

_{1}X

_{2}; where X

_{1}and X

_{2}are not necessarily distinct.

Determine the possible positive integer values of M, with 2 ≤ M ≤ 101, such that this equation has at least one valid solution.

X

_{1}

^{2}+ X

_{2}

^{2}= X

_{1}X

_{2}

__Note__: X

_{1}X

_{2}denotes the concatenation of the two digits.