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.

 10   for Base=3 to 100
 20   for X=1 to Base-1:H=X*Base*Base
 30   for Y=1 to Base-1:T=Y*Base
 40   for Z=1 to Base-1:U=Z
 50     if H+T+U=X^X+Y^Y+Z^Z then print Base;X;Y;Z,H+T+U
 60   next
 70   next
 80   next
 90   next

base x1 x2 x3    decimal value lhs & rhs
 4    1  3  1        29
 4    3  1  3        55
25    5  1  3      3153
91    6  1  5     49782

 

Posted by Charlie on 2009-04-13 02:55:02