Each of x₁, x₂ and x₃ corresponds to a nonzero digit, whether same or different, in positive integer base b.

Determine all possible value(s) of b ≤ 100 such that this equation has at least one valid solution:

x₁x₂x₃ = x₁^x₁ + x₂^x₂ + x₃^x₃

Note: x₁x₂x₃ corresponds to concatenation of the three digits.

base 4 has these 2 solutions 131,313

base 5 has only 1 solution as 513

base 91 has only 1 solution as 615

I used Mathematica to check every 3 digit base b number for each b<=100 with no digits being 0.

Posted by Daniel on 2009-04-12 17:06:14