List questions from quadratic-residues

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Prove or disprove a claim involving Pythagorean primes

Published on 05 Feb 2017 - 12:12

125

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$p \mid q^r+1$, Prove that either $2r\mid p-1$ or $p \mid q^2-1$

Published on 05 Feb 2017 - 20:06

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Is $x^2 \equiv -1 \pmod{365}$ solvable?

Published on 07 Feb 2017 - 16:09

72

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Smallest prime that is a quadratic residue modulo a fixed prime

Published on 14 Feb 2017 - 19:45

256

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How to deduce the number of solutions?

Published on 03 Mar 2017 - 23:31

119

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

Published on 25 Mar 2026 - 12:48

131

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Legendre Symbol by Fermat's little theorem.

Published on 25 Mar 2026 - 19:10

178

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Roots of a quadratic equation modulo p

Published on 10 Mar 2017 - 19:45

96

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$4n$ is a square modulo $d$ implies $n$ is a square modulo $d$

Published on 13 Mar 2017 - 11:49

64

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

Published on 25 Mar 2026 - 12:46

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Nonzero integers mod $p$ - showing exactly half are perfect squares

Published on 15 Mar 2017 - 17:25

474

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Proof that $y^2=x^3+21$ has no integral solution with elementary methods?

Published on 24 Mar 2026 - 23:43

857

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Computing the Jacobi symbol

Published on 23 Feb 2026 - 4:33

828

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Finding all solutions of $x^{11}\equiv 1\bmod23,$

Published on 24 Mar 2017 - 11:36

List Question

How to calculate a number of $x$ values such that $f(x)$ is a quadratic residue modulo $m$?

Prove or disprove a claim involving Pythagorean primes

$p \mid q^r+1$, Prove that either $2r\mid p-1$ or $p \mid q^2-1$

Is $x^2 \equiv -1 \pmod{365}$ solvable?

Smallest prime that is a quadratic residue modulo a fixed prime

How to deduce the number of solutions?

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

Legendre Symbol by Fermat's little theorem.

Roots of a quadratic equation modulo p

$4n$ is a square modulo $d$ implies $n$ is a square modulo $d$

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

Nonzero integers mod $p$ - showing exactly half are perfect squares

Proof that $y^2=x^3+21$ has no integral solution with elementary methods?

Computing the Jacobi symbol

Finding all solutions of $x^{11}\equiv 1\bmod23,$

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