(In reply to re: Answer:
Ch & SH,
Take a composite n like 15 (I have chosen an odd number).
A repunit of 15 ones looks like 111 111 111 111 111 (spaces
introduced to illustrate my point)
or like 11111 11111 11111, and now you see that it is divisible by 111 and by 11111 in any base.
For formal proof replace 15=5*3 by n=p*q