The 27-digit number 380022607743740081787109376 has an interesting property:
3800226077437400817871093762 = 144417182396352539175410357380022607743740081787109376
That is, the last 27 digits of 3800226077437400817871093762 are also "380022607743740081787109376".
There is one other 27-digit number with this property (no, twenty-six '0's followed by a 1 or another 0 don't count). What is it?
Advanced: prove that there's only one other 27-digit number like this.
Advanced-advanced: prove that we can't do something like this in binary or hexadecimal.