Is $f = x^2 + y^2$ reducible polynomial over the finite field $f$ of order 11?
2026-04-04 18:36:30.1775327790
reducible polynomial over the finite field of order 11
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Hint: $11 \equiv 3$ mod $4$, hence $11$ cannot be written as sum of two squares, or equivalently, $-1$ is not a square in $\mathbb{F}_{11}$.