Your Japanese co-worker from this problem hands you another piece of paper one day:
1820143 2383341 3245353 8425463 6354607
6627972 9088779 7839589 ??????? ???????
What two seven-digit numbers come after the ones given?
On the back of the paper is a hint:
You get stuck, and ask your co-worker for another hint.
He simply writes a zero in front of the existing hint, leaving you with a note that reads:
Again, he just scribbles a plus sign in front of the zero, leaving you with a note that reads:
And a fourth:
This time, he writes a whole row of numbers on the bottom:
12 34 56 71 23 45 67
And a fifth:
He crosses out the 71 23 45 67 and writes 78 9A BC DE in its place.
And a sixth:
He writes "COUNTER MODE" next to the "+03".
And a seventh, just as clarification:
Each letter is exactly two digits long.
I promise this one doesn't involve any obscure numbers like 264, or any other such esoteric facts, unlike my last one in this regard. Everything here is simple mathematics and logic.