Solvability of $x^4+x^3+x^2+x+1\equiv 0 \pmod p$ implies $p\equiv 1 \pmod 5$; infinitely many primes $5n+1$

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Solvability of $x^4+x^3+x^2+x+1\equiv 0 \pmod p$ implies $p\equiv 1 \pmod 5$; infinitely many primes $5n+1$ · Prove2Me