$10^{x} \mod 7 (x>=0)$ has a period of 6: $1, 3, 2, 6, 4, 5, 1...$
The sum of the first 6 numbers is 21 which is divisible by 7 therefore $dddddd$ is also divisible by 7 and hence n-digit numbers (where n is divisible by 6 and all digits are the same) is also divisible by 7 because the period is 6.
$10^{x} \mod 7 (x>=0)$ has a period of 6: $1, 3, 2, 6, 4, 5, 1...$
The sum of the first 6 numbers is 21 which is divisible by 7 therefore $dddddd$ is also divisible by 7 and hence n-digit numbers (where n is divisible by 6 and all digits are the same) is also divisible by 7 because the period is 6.