All reports by Author Kiran Kedlaya:

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TR23-177
| 18th November 2023
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Kiran Kedlaya, Swastik Kopparty#### On the degree of polynomials computing square roots mod p

Kiran Kedlaya, Swastik Kopparty

For an odd prime $p$, we say $f(X) \in {\mathbb F}_p[X]$ computes square roots in $\mathbb F_p$ if, for all nonzero perfect squares $a \in \mathbb F_p$, we have $f(a)^2 = a$.

When $p \equiv 3$ mod $4$, it is well known that $f(X) = X^{(p+1)/4}$ computes square ...
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