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.

131₄  =  29   = 1¹ + 3³ + 1¹
313₄  =  55   = 3³ + 1¹ + 3³
513₂₅ = 3153  = 5⁵ + 1¹ + 3³
615₉₁ = 49782 = 6⁶ + 1¹ + 5⁵

The values of b are 4, 25, and 91.

Posted by Dej Mar on 2009-04-12 21:41:33