Answer:
Explanation:
very interesting question. The temptation is to say that n should be 11 and that likely is divisible by 11 but it may not be the smallest.
100 + 100^2 = 100 + 10000 = 10100
The pattern of the series goes 101010101 ... 00...
100 / 11 = The remainder is 1/11
10100 / 11 = the remainder is 2/11
1010100 /11 the remainder is 3/11
The pattern suggests that the remainder will be 0 then n = 11
There might be other ways of doing this, but I don't know them.