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Sum number equals integer (Posted on 2011-06-11) Difficulty: 3 of 5
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?

No Solution Yet Submitted by K Sengupta    
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Nice start | Comment 2 of 5 |
Nice start, Jer.

One stray observation, which may or may not be useful, is that the left side of the equation = 0 (mod x-1)
 
This means that the right side also = 0 (mod x-1).

By casting out x-1's, this means that 
 (I + n + t + e + g + e + r) = 0 mod (x-1)

  Posted by Steve Herman on 2011-06-14 21:20:01
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