List questions from quadratic-residues

Published on 27 Apr 2018 - 11:01

79

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Confusion about sum of squares.

Published on 22 Mar 2026 - 1:35

1k

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Show that the quadratic congruence $x^2+x+1≡0$ (mod p) has an integer solution iff -3 is a QR modulo p.

Published on 21 May 2018 - 10:10

896

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Show that if a is a QR mod p and q then a is a QR mod pq

Published on 25 Mar 2026 - 9:29

29

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Is the n-th odd prime, which has 2 as nonresidue, polynomially bounded by n * ln(n)?

Published on 31 May 2018 - 17:56

1.3k

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Number of solutions to the congruence $x^2\equiv 121\pmod {1800}$

Published on 04 Jun 2018 - 9:18

72

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finite field quadratic residue "counterpart"

Published on 04 Jun 2018 - 22:55

129

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Independence of shifted squares mod p

Published on 06 Jun 2018 - 15:23

211

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$n^2 \equiv (p-1) \mod p$ where $p$ is a Pythagorean prime.

Published on 08 Jun 2018 - 5:23

2.5k

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A square modulo every prime is a square. Proof valid?

Published on 12 Jun 2018 - 7:48

55

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Distribution of non-negative $y$ in OEIS A205535

Published on 25 Mar 2026 - 22:04

61

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Prove that numbers divisible by $p$ but not by $p^2$ are quadratic non-residues of $p^n$

Published on 28 Jun 2018 - 3:53

1.6k

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Find the set of primes $p$ which $6$ is a quadratic residue $\mod p$

Published on 17 Mar 2026 - 11:59

343

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square roots in multiplicative group of integers modulo n

Published on 30 Jun 2018 - 13:22

226

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Find smallest prime $p$ such that all primes $q < 40$ are quadratic non-residues $\pmod p$

Published on 06 Jul 2018 - 19:19

List Question

Number of solutions in equation $x^2 \equiv a \mod(pq)$

Confusion about sum of squares.

Show that the quadratic congruence $x^2+x+1≡0$ (mod p) has an integer solution iff -3 is a QR modulo p.

Show that if a is a QR mod p and q then a is a QR mod pq

Is the n-th odd prime, which has 2 as nonresidue, polynomially bounded by n * ln(n)?

Number of solutions to the congruence $x^2\equiv 121\pmod {1800}$

finite field quadratic residue "counterpart"

Independence of shifted squares mod p

$n^2 \equiv (p-1) \mod p$ where $p$ is a Pythagorean prime.

A square modulo every prime is a square. Proof valid?

Distribution of non-negative $y$ in OEIS A205535

Prove that numbers divisible by $p$ but not by $p^2$ are quadratic non-residues of $p^n$

Find the set of primes $p$ which $6$ is a quadratic residue $\mod p$

square roots in multiplicative group of integers modulo n

Find smallest prime $p$ such that all primes $q < 40$ are quadratic non-residues $\pmod p$

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