Solvability of $x^2+x+1\equiv 0 \pmod p$ implies $p\equiv 1 \pmod 6$; infinitely many primes $6k+1$

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Solvability of $x^2+x+1\equiv 0 \pmod p$ implies $p\equiv 1 \pmod 6$; infinitely many primes $6k+1$ · Prove2Me