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Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology.
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Polynomial that is not always a square over $\mathbb{Z}_p$
Let $p > 3$ be prime. Is is true that there exists $x \in \mathbb{Z}_p$ such that
$$
(1+x^2)^3-1
$$
is not a square in $\mathbb{Z}_p$? In particular, when $-1$ is not a square in $\mathbb{Z}_p$, can w …