List questions from quadratic-residues

Published on 12 Nov 2013 - 20:09

231

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Quadratic Residues

Published on 12 Nov 2013 - 20:41

130

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Reduction of the question of quadratic residues mod $m$ to the primary decomposition of $m$.

Published on 14 Nov 2013 - 15:43

1.9k

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Prove ab is a quadratic residue mod p

Published on 14 Nov 2013 - 23:36

694

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Show that when $a$ is a quadratic nonresidue, $a-1$ is a quadratic residue.

Published on 15 Nov 2013 - 21:10

1k

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Consecutive quadratic residues of primes that differ by 2

Published on 19 Nov 2013 - 2:15

305

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Find solutions to equation (ring/field theory, residue class)

Published on 29 Nov 2013 - 7:36

2.4k

Views

Find all primes $p$ such that $14$ is a quadratic residue modulo $p$.

Published on 30 Nov 2013 - 3:26

9.1k

Views

Relationship between primitive roots and quadratic residues

Published on 01 Dec 2013 - 23:50

75

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Let $Q = \{a:{1\le a\le p-1 \text{ and } a \text{ is a quadratic residue}}\}$. Prove that if $p\ge 5$, then $\sum_{t\in Q} t \equiv 0 \pmod{p}$.

Published on 09 Dec 2013 - 17:19

829

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Quadratic Residues, stating at least $2,5$ or $10$.

Published on 19 Dec 2013 - 5:15

2.7k

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What is the point of quadratic residues?

Published on 26 Mar 2026 - 1:34

241

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Quadratic residues and kernel of a homomorphism

Published on 31 Dec 2013 - 17:37

628

Views

Why is raising by $(p-1)/2$ not always equal to $1$ in $\mathbb{Z}^*_p$? (Manipulating powers modulo p)

Published on 09 Jan 2014 - 1:43

196

Views

Probabilistic time algorithm for finding the solution for quadratic congruences (case when p is prime)

Published on 11 Jan 2014 - 22:37

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Distribution of Quadratic Residues

Quadratic Residues

Reduction of the question of quadratic residues mod $m$ to the primary decomposition of $m$.

Prove ab is a quadratic residue mod p

Show that when $a$ is a quadratic nonresidue, $a-1$ is a quadratic residue.

Consecutive quadratic residues of primes that differ by 2

Find solutions to equation (ring/field theory, residue class)

Find all primes $p$ such that $14$ is a quadratic residue modulo $p$.

Relationship between primitive roots and quadratic residues

Let $Q = \{a:{1\le a\le p-1 \text{ and } a \text{ is a quadratic residue}}\}$. Prove that if $p\ge 5$, then $\sum_{t\in Q} t \equiv 0 \pmod{p}$.

Quadratic Residues, stating at least $2,5$ or $10$.

What is the point of quadratic residues?

Quadratic residues and kernel of a homomorphism

Why is raising by $(p-1)/2$ not always equal to $1$ in $\mathbb{Z}^*_p$? (Manipulating powers modulo p)

Probabilistic time algorithm for finding the solution for quadratic congruences (case when p is prime)

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