List questions from quadratic-reciprocity

Published on 06 Dec 2016 - 15:23

78

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Show that for any prime p, there are integers $x, y$ such that $p| x^2+y^2+1$

Published on 07 Dec 2016 - 20:45

96

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Relation between reciprocity laws and split places

Published on 25 Dec 2016 - 10:00

190

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$2$ is a primitive root of $p = 2q+1$ when $p = 8t+3$

Published on 03 Jan 2017 - 18:49

152

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Using Gauss's Lemma to determine primes of a quadratic residue

Published on 11 Feb 2017 - 5:29

308

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$n^6$ does not divide $6^n$

Published on 21 Feb 2017 - 15:14

118

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Solve $ x^2 \equiv 3 \pmod {10007}$ using quadratic reciprocity

Published on 05 Mar 2017 - 1:45

349

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Prove that the Zolotarev symbol is the same as Legendre and Jacobi symbols

Published on 05 Mar 2017 - 19:51

63

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Why $\sqrt p \in\mathbb Q(\xi_p)$?

Published on 15 Mar 2017 - 4:35

1k

Views

For any prime $p$ of the form $4k + 3$, prove that $x^2 + \frac{p+1}{4} \equiv 0 \;(\text{mod }p)$ is not solvable

Published on 23 Feb 2026 - 4:43

149

Views

Show that set of reduced residue classes is a subgroup of the multiplicative group of reduced residue classes

Published on 23 Feb 2026 - 4:42

953

Views

How do I use the Law of Quadratic Reciprocity to solve a congruence?

Published on 29 Mar 2017 - 15:59

293

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Quadratic residues mod 100000

Published on 03 Apr 2017 - 1:43

155

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Proofs regarding cubic reciprocity

Published on 25 Mar 2026 - 11:09

138

Views

Proof of quadratic reciprocity from Artin reciprocity

Published on 02 Feb 2023 - 18:31

List Question

show that if p is a prime divisor of $839$ and $(5/p)=1$ then $839$ is a prime number

Show that for any prime p, there are integers $x, y$ such that $p| x^2+y^2+1$

Relation between reciprocity laws and split places

$2$ is a primitive root of $p = 2q+1$ when $p = 8t+3$

Using Gauss's Lemma to determine primes of a quadratic residue

$n^6$ does not divide $6^n$

Solve $ x^2 \equiv 3 \pmod {10007}$ using quadratic reciprocity

Prove that the Zolotarev symbol is the same as Legendre and Jacobi symbols

Why $\sqrt p \in\mathbb Q(\xi_p)$?

For any prime $p$ of the form $4k + 3$, prove that $x^2 + \frac{p+1}{4} \equiv 0 \;(\text{mod }p)$ is not solvable

Show that set of reduced residue classes is a subgroup of the multiplicative group of reduced residue classes

How do I use the Law of Quadratic Reciprocity to solve a congruence?

Quadratic residues mod 100000

Proofs regarding cubic reciprocity

Proof of quadratic reciprocity from Artin reciprocity

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