I'm solving a problem in group theory. A key argument in my attempt is to assess if the following statement is true.

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> Let $p$ be a prime number. For all $1 \le k,r < p$, there exists $n \in \mathbb N$ such that $nk \equiv r \pmod{p}$.
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I tested for some small numbers on MS Excel for which it holds true. Could you please elaborate if it's actually true? Thank you so much!