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 respective minimum and maximum positive integer value of M, with M < 100, such that this equation has at least one valid solution.

X₁^X₁ + X₂^X₂ + X₃^X₃ = X₁X₂X₃ - 1

Note: X₁X₂X₃ denotes the concatenation of the three digits.

323 BASE 4 FOR ONE

THERE MIGHT BE ADDIIONAL SOLUTIONS

Posted by Ady TZIDON on 2009-10-22 15:39:24