#Show that a prime number other than 2 and 3 is congruent to 1 or -1 modulo 6

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sturdy bridge
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Can you help me for this
for me in i'm here

fading topazBOT
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Show that a prime numer other than 2 and 3 is congruent to 1 or -1 modulo 6

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Show that a prime number other than 2 and 3 is congruent to 1 or -1 modulo 6

brittle steppe
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here is my attempt:

Because $p \in \mathbb{P}\setminus{2,3}$, then $\mathrm{coprime}(p,6)$. Therefore, there exists a modular inverse $x$ of $p$ such that:

$$xp \equiv_6 1$$

shy locustBOT