Let x be the first number in the arithmetic sequence
and y be the difference
The numbers are:
A, B , C
x, x+y, x+2y
We add all to check if it is divisible by 3 or 9
[tex]x+x+y+x+2y=3x+3y=3(x+y)[/tex]
Therefore in in the number ABCABC one factor is 3
ABCABC is divisible by 1001 because [tex]ABCABC/1001=ABC[/tex]
Therefore there are two numbers that are always factors of ABCABC which are 3 and 1001, therefore the largest integer that divide all numbers in the form ABCABC is 3*1001 or 3003
