List questions from quadratic-residues

Published on 23 Mar 2018 - 19:17

130

Views

If $a$ and $-a$ are both quadratic residues mod an odd prime $p$, then $p \equiv 1\pmod4$

Published on 24 Mar 2018 - 5:23

390

Views

Solve $x^2 \equiv 1 \pmod{30}$ and generalize.

Published on 28 Mar 2018 - 17:44

505

Views

Question regarding quadratic residue

Published on 02 Apr 2018 - 12:03

253

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Is there a univariate rational polynomial which represents only squares in $\mathbb{R}$ and $\mathbb{Q}_2$, but not all other $\mathbb{Q}_p$?

Published on 25 Mar 2026 - 9:28

233

Views

No canonical non-quadratic residue for primes $\equiv 1 \bmod 8$?

Published on 04 Apr 2018 - 17:44

40

Views

Solving the following congruence

Published on 05 Apr 2018 - 0:13

325

Views

Number of solutions to a congruence equation

Published on 25 Mar 2026 - 10:57

103

Views

Prove that $a^2,a^4,...,a^{p-1}$ are the quadratic residues modulo $p$.

Published on 24 Mar 2026 - 7:21

1.2k

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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 25 Mar 2026 - 4:19

445

Views

Determine all primes $p > 5$ such that 10 is a quadratic residue mod p

Published on 08 Apr 2018 - 20:25

64

Views

Need counterexample for some facts related with Quadratic residues

Published on 11 Apr 2018 - 9:37

253

Views

Quadratic Residue Problem: $2x^2+1\equiv 0\mod p$

Published on 14 Apr 2018 - 9:58

111

Views

iff condition for quadratic residue modulo p when $p\equiv3\mod 4$

Published on 25 Mar 2026 - 13:53

264

Views

Quadratic residue $a \pmod{pq}$

Published on 24 Apr 2018 - 12:58

List Question

Find all quadratic residues modulo $15$.

If $a$ and $-a$ are both quadratic residues mod an odd prime $p$, then $p \equiv 1\pmod4$

Solve $x^2 \equiv 1 \pmod{30}$ and generalize.

Question regarding quadratic residue

Is there a univariate rational polynomial which represents only squares in $\mathbb{R}$ and $\mathbb{Q}_2$, but not all other $\mathbb{Q}_p$?

No canonical non-quadratic residue for primes $\equiv 1 \bmod 8$?

Solving the following congruence

Number of solutions to a congruence equation

Prove that $a^2,a^4,...,a^{p-1}$ are the quadratic residues modulo $p$.

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 $p$

Determine all primes $p > 5$ such that 10 is a quadratic residue mod p

Need counterexample for some facts related with Quadratic residues

Quadratic Residue Problem: $2x^2+1\equiv 0\mod p$

iff condition for quadratic residue modulo p when $p\equiv3\mod 4$

Quadratic residue $a \pmod{pq}$

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