help

see the thing here is that

10¹⁶-1 is divisible by 17

Look at fermat's theorem which has been discussed many times here...

So we can say that 999999.... (17 times) is divisible by 17

so if you divide this by 9, nothign will change.

So 111... (16 times) is divisible by 17

so 1111... (32 times) is divisible by 17..

111...(32 times) = 100 x 111.. .(30 times)+11

LHS is divislbe by 17, so RHS is also divisible by 17

but 11 is not.. so the number is not divisible.