<s>[INST] If $x\equiv2\pmod{3}$ prove that $3|4x^2+2x+1$ I've tried many different things to get a factor of $k-2$ but keep failing.
If $x\equiv2\pmod{3}$ prove that $3 \mid 4x^2+2x+1$
 [/INST] Since $x \equiv 2 \pmod 3$,
$4x^2+2x+1 \equiv (16) + (4) + (1) \equiv 21 \equiv 0 \pmod 3$
Hence, $3\mid4x^2+2x+1$.
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