Odd Power of 2 is Congruent to 2 Modulo 3

Theorem
Let $n \in \Z_{\ge 0}$ be an odd positive integer.

Then:
 * $2^n \equiv 2 \pmod 3$

Proof
From Congruence Modulo 3 of Power of 2:
 * $2^n \equiv \left({-1}\right)^n \pmod 3$

We have that $n$ is odd.

Hence:

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