Proof
(related to Proposition: Coprime Primes)
 $p$ is by hypothesis a prime, therefore it has only the divisors $1$ and $p.$
 Since by hypothesis $p\not\mid n$, the greatest common divisor equals $\gcd(p,n)=1.$
 This, by definition, means that $p$ and $n$ are coprime.
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References
Bibliography
 Landau, Edmund: "Vorlesungen über Zahlentheorie, Aus der Elementaren Zahlentheorie", S. Hirzel, Leipzig, 1927