A problem that gives me problems

I came across this while doing extra research and I can't seem to get the answer... help me please

Qu: Find as a sum of powers of 10, an odd, positive integer n, such that when ab is multiplied by n, the resulting number has 2k digits and the sum of its digits is divisible by k (where k is a positive integer)

An odd number constructed from a sum of powers of ten requires an odd quantity (say, one) of the powers of ten to be , no?

What is " "?

ab is any number... the question is structured in such a way that you cannot substitute numbers into ab to prove the answer.