 |
| ||
| |||
|
| Math Central | Quandaries & Queries |
|
Question from Steve, a student: The difference of the two numbers 'abcdef ' and ' fdebca ' is divisible by Thanks. |
Use the fact that 100000 = 369*271 + 1, that is 100000%271 = 1.
Now
(abcdef - fdebca)%271 =
[(a-f)*100000 + (b-d)*10000 + (c-e)*1000 + (d-b)*100 + (e-c)*10 + (f-a)]%271.
Since 100000%271 = 1, the first and last summand cancel out, and you are left with
[(b-d)*(10000-100) + (c-e)(1000 - 10)]%271.
We have (10000-100)%271 = 144 and (1000 - 10)%271 = 177, while (b-d), (c-e) 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
| ||
| ||
| ||
 |
 |
|
Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.