Each of X₁ and X₂ represents a nonzero digit of the 2-digit base M positive integer X₁X₂; where X₁ and X₂ 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.

X₁² + X₂² = X₁X₂

Note: X₁X₂ denotes the concatenation of the two digits.

The non-compliant numbers are those such that n^2+1 is prime; A005574 in Sloane, but I was not able to determine the explanation for this, Ideas, anyone?

Posted by broll on 2011-07-28 14:14:13