List questions from legendre-symbol

Published on 14 Apr 2026 - 16:43

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Let $p$ be an odd prime. Suppose $a$ and $b$ are both primitive roots mod $p$. Show that $ab$ is not a primitive root mod $p$

Published on 17 Apr 2026 - 11:04

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Suppose $p$ is $3\bmod 4$. Show $a$ and $-a$ cannot both be primitive roots $\bmod p$.

Published on 17 Apr 2026 - 0:49

102

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Legendre symbol related-problem

Published on 14 Apr 2026 - 23:37

186

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Legendre symbol question without Euler's Criterion

Published on 16 Apr 2026 - 12:27

1.8k

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Legendre symbol of $(-2/p)$.

Published on 15 Apr 2026 - 7:57

3.1k

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Legendre symbol of $(-3/p)$.

Published on 15 Apr 2026 - 21:21

133

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Determine $p$ such that $x^2 \equiv a \pmod{p}$ using Legendre symbols(for specific values of $a$)

Published on 14 Apr 2026 - 3:25

262

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$N$ square-free $\Rightarrow \exists a \in (\mathbb Z / N\mathbb Z)^{\times}, (\frac{a}{N}) = -1$

Published on 21 Apr 2026 - 10:45

410

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Every prime divisor ($p \neq 5$) of $n^2+n-1$ is of the form $10k+9$

Published on 16 Apr 2026 - 15:43

74

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Determine $\left ( \frac{5}{p} \right )=1$ in a different way

Published on 16 Apr 2026 - 6:32

161

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Quadratic Reciprocity problem.. help!

Published on 28 Apr 2026 - 9:06

672

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How can $\left(\frac pq\right)\left(\frac qp\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}$

Published on 16 Apr 2026 - 12:43

1.6k

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$-3$ is a quadratic residue iff $p \equiv 1 \pmod 3$

Published on 15 Apr 2026 - 14:29

63

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How to guarantee non existence of order 4 elements in class group of a maximal order

Published on 07 May 2026 - 9:19

List Question

Elementary Number Theory: Legendre Symbol

Let $p$ be an odd prime. Suppose $a$ and $b$ are both primitive roots mod $p$. Show that $ab$ is not a primitive root mod $p$

Suppose $p$ is $3\bmod 4$. Show $a$ and $-a$ cannot both be primitive roots $\bmod p$.

Legendre symbol related-problem

Legendre symbol question without Euler's Criterion

Legendre symbol of $(-2/p)$.

Legendre symbol of $(-3/p)$.

Determine $p$ such that $x^2 \equiv a \pmod{p}$ using Legendre symbols(for specific values of $a$)

$N$ square-free $\Rightarrow \exists a \in (\mathbb Z / N\mathbb Z)^{\times}, (\frac{a}{N}) = -1$

Every prime divisor ($p \neq 5$) of $n^2+n-1$ is of the form $10k+9$

Determine $\left ( \frac{5}{p} \right )=1$ in a different way

Quadratic Reciprocity problem.. help!

How can $\left(\frac pq\right)\left(\frac qp\right)=(-1)^{\frac{p-1}{2}\frac{q-1}{2}}$

$-3$ is a quadratic residue iff $p \equiv 1 \pmod 3$

How to guarantee non existence of order 4 elements in class group of a maximal order

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