



 
Use the fact that 100000 = 369*271 + 1, that is 100000%271 = 1. Now
Since 100000%271 = 1, the first and last summand cancel out, and you are left with
We have (10000100)%271 = 144 and (1000  10)%271 = 177, while (bd), (ce) are between 9 and 9. You only need to check that x*144 + y*177 is never a multiple of 271 when x and y are integers from 9 to 9. Claude  


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