Is $x^4-1$ reducible over every $\mathbb{F}_p$ for every prime p? I think I need to split into the cases of $p=2$ and $p$ being odd, but not idea how to proceed from there...
2026-04-06 15:08:24.1775488104
Is $x^4-1$ reducible over every $\mathbb{F}_p$ for every prime p?
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Yes, because $x^4 - 1 = (x-1)(x^3 + x^2 + x + 1).$