List questions from quadratic-residues

Published on 16 Apr 2026 - 16:22

133

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

Published on 16 Apr 2026 - 17:46

393

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

Published on 17 Apr 2026 - 10:04

509

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Question regarding quadratic residue

Published on 14 Apr 2026 - 19:56

254

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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 16 Apr 2026 - 12:22

236

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

Published on 16 Apr 2026 - 1:54

44

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Solving the following congruence

Published on 10 Apr 2026 - 3:56

327

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Number of solutions to a congruence equation

Published on 11 Apr 2026 - 18:33

106

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

Published on 06 May 2026 - 23:55

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 10 May 2026 - 12:34

448

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

Published on 15 Apr 2026 - 16:51

68

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Need counterexample for some facts related with Quadratic residues

Published on 16 Apr 2026 - 20:40

256

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

Published on 17 Apr 2026 - 13:50

113

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

Published on 16 Apr 2026 - 10:00

268

Views

Quadratic residue $a \pmod{pq}$

Published on 13 Apr 2026 - 19:22

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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