# Tagged Questions

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### Chowla's Construction of prime having least quadratic non-residue $\gg \log p$

This paper by NC Ankeny mentions that " S. Chowla has proved that there exist infinitely many primes $k$ where the first $c_1\log k$ residues $(\bmod k)$ are all quadratic residues". I recently ...
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### Given n and q, how to find p so q$\neq$n-th power (mod p)?

Reasonable exceptions allowed on $q$. Example solution: $n=2$. Suppose $q$ is odd. Let $p$ be so $pq\equiv -1$ (mod 8). Then $q\neq$ 2nd power (mod $p$) is the same as $\left(\frac{q}{p}\right)=-1$...
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### Computation of Hilbert symbol of order 4

We have explicit expressions for the quadratic Hilbert symbol over $\mathbb Q$, for example $\left(\dfrac{x,y}2\right)_2=(-1)^{\frac{x-1}2\frac{y-1}2} (x,y\ne2)$. Are similar expressions known for the ...
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### Can Eisenstein's lattice point proof of quadratic reciprocity be generalized?

I'm referring to this proof. The key formula ("Eisenstein's Lemma") is $$\left(\frac{q}{p}\right)=(-1)^{\sum_{u}\lfloor\frac{qu}{p}\rfloor},\text{ where u=2,4,\ldots,p-1}$$ The sum in the exponent ...
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### Context for “Coronidis Loco” from Weil's Basic Number Theory

In Samuel James Patterson's article titled Gauss Sums in The Shaping of Arithmetic after C. F. Gauss’s Disquisitiones Arithmeticae, Patterson says "Hecke [proved] a beautiful theorem on the different ...
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### What's the “best” proof of quadratic reciprocity?

For my purposes, you may want to interpret "best" as "clearest and easiest to understand for undergrads in a first number theory course," but don't feel too constrained.