P-adic Norm not Complete on Rational Numbers/Proof 2/Lemma 1
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Theorem
Let $p$ be a prime number.
Then:
- $\exists x \in \Z_{>0}: p \nmid x, x \ge \dfrac {p + 1} 2$
Proof
Let $x = p + 1$.
Then $p \nmid x$ and:
- $x = p + 1 > p > 0$
$\blacksquare$