Imagine a number N which is made of digits d repeating n times
eg:

$$$N = dddddd.....d$$$ (n times) if we keep taking modulo of $$$N$$$(increase the number of digits) with some number $$$p$$$ at one point the modulo keeps on repeating eg: $$$d = 3$$$ and $$$p = 7$$$

Row Number	N	N mod 7
1	3	3
2	33	5
3	333	4
4	3333	1
5	33333	6
6	333333	0
7	3333333	3
8	33333333	5
9	333333333	4
10	3333333333	1
11	33333333333	6

From row 7 it keeps repeating
The reason i am asking this question due to this Problem

Is there any proof to this or is it just that I have to remember this.

It my first time encountering this pattern