List questions from quadratic-residues

Published on 10 May 2026 - 12:12

77

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Number of solution is twice $(x,y)$

Published on 17 Apr 2026 - 18:27

705

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Prove $\sum\limits_{j=1}^{p-1} j\left(\frac{j}{p}\right) = 0 $ for an odd prime $p$ with $p\equiv 1\text{ mod } 4$

Published on 29 Apr 2026 - 12:46

251

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Understanding quadratic reciprocity

Published on 10 May 2026 - 11:31

115

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Show that there's a solution to $x^2 \equiv -1 \pmod {p^2}$

Published on 20 Apr 2026 - 15:21

41

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Number of solutions for quadratic polynomials in $\mathbb{F}_p$

Published on 20 Apr 2026 - 7:26

138

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The existence of a solution of a quadratic congruence modulo $p$

Published on 10 May 2026 - 9:25

306

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How many quadratic residues of $\mathbb{F}_{p^n}$ are in the kernel of a morphism $\mathbb{F}_{p^n}^+\to \mathbb{F}_p^+$?

Published on 20 Apr 2026 - 11:48

55

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A question about the Legendre symbol $\left(\frac{1+a}{p}\right)$

Published on 28 Apr 2026 - 15:34

182

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How many $k$ satisfy the equation $(p \cdot k)^2 \equiv 0 \pmod{p^n}$ where $k < p^n$ and $p$ is prime

Published on 28 Apr 2026 - 6:37

215

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Is there finite number of $p$ such $\sum_{k=1}^{p-1}\left\{\frac{k^2}{p}\right\}=\frac{p-3}{2}？$

Published on 10 May 2026 - 9:30

82

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One question about quadratic residue

Published on 10 May 2026 - 12:36

53

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Help regarding quadratic residue

Published on 10 May 2026 - 12:36

1k

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Is $x^2 \equiv 1 \pmod{p^k} \iff x \equiv \pm 1 \pmod {p^k}$ for odd prime $p$?

Published on 10 May 2026 - 12:39

828

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Quadratic Residues Proof

Published on 10 May 2026 - 12:36

List Question

Prove: $k^2 \equiv 1 \mod p \implies k \equiv \pm1 \mod p$

Number of solution is twice $(x,y)$

Prove $\sum\limits_{j=1}^{p-1} j\left(\frac{j}{p}\right) = 0 $ for an odd prime $p$ with $p\equiv 1\text{ mod } 4$

Understanding quadratic reciprocity

Show that there's a solution to $x^2 \equiv -1 \pmod {p^2}$

Number of solutions for quadratic polynomials in $\mathbb{F}_p$

The existence of a solution of a quadratic congruence modulo $p$

How many quadratic residues of $\mathbb{F}_{p^n}$ are in the kernel of a morphism $\mathbb{F}_{p^n}^+\to \mathbb{F}_p^+$?

A question about the Legendre symbol $\left(\frac{1+a}{p}\right)$

How many $k$ satisfy the equation $(p \cdot k)^2 \equiv 0 \pmod{p^n}$ where $k < p^n$ and $p$ is prime

Is there finite number of $p$ such $\sum_{k=1}^{p-1}\left\{\frac{k^2}{p}\right\}=\frac{p-3}{2}？$

One question about quadratic residue

Help regarding quadratic residue

Is $x^2 \equiv 1 \pmod{p^k} \iff x \equiv \pm 1 \pmod {p^k}$ for odd prime $p$?

Quadratic Residues Proof

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