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?

Jer noted "If r is not zero, r+r has a carry so for e+e to end in r, r must be odd."  When this is true then the base x is of the form 4y+2.

4y-1 4y      2  y      1  y   2y+1
+    4y   4y-2 4y+1  y-1  y   2y+1
----------------------------------
4y   4y-2 4y+1  y-1  y   2y+1    0

Posted by Brian Smith on 2016-12-19 13:59:26