Each of the small letters in bold represents a different base x digit from 0 to x-1 to satisfy this alphametic equation. None of the numbers can contain any leading zero.

                              (x-1)*number = integer

Determine the minimum positive integer value of x such that the above equation has at least one solution. What is the next smallest value of x having this property?

(In reply to Parametric solutions by Brian Smith)

Let z=x/2.  Then a parametric solution for all even bases starting with x=14 is:

2z-4 2z-3    3  z     1 z 0
+    2z-3 2z-6 2z-2 z-2 z 0
---------------------------
2z-3 2z-6 2z-2  z-2 z   0 0

Posted by Brian Smith on 2016-12-21 12:18:56