I'm not mathematician so I can't write it down in mathematical language, and I can only explain rambling words with almost no mathematical language...

I'm re-posting this problem, because my former question was closed, and I don't know what to do about that.

So, the basic rule is this.

Choose a prime number $p$ greater than $5$

ex) $p=7$

Calculate $\frac{1}{p}$ and find the number of repeating decimal digits. Call this $r.$

ex) when $p=7, r=6$

Find all the divisors of $r,$ except $r$ itself, and name them $r\_i.$

ex)when $r=6, r\_1=1, r\_2=2, r\_3=3$

Choose any $r\_x.$

ex) $r\_x=3$

Choose any random $r\_x$-digit number, and name it $n.$

ex) when $r\_x=3, n=171$

Concatenate $n$ with itself several times to create an $r$ digit number (always possible since $r\_x$ is the divisor of $r$), and name it $N$
ex) when $n=171, N=171171$

This final number $N$ you created will be divided by the prime number you chose without remainder.

ex)$\frac{171171}{7}=24453$

Is this always true?

for the understanding, I made a video explaining about what I found.

<https://www.youtube.com/watch?v=g1ZzXkQeN0I>

Hope this is not against the policy of this page.