List questions from quadratic-residues

Published on 31 Jan 2013 - 22:12

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Computing the Legendre symbol $\bigl(\frac{3}{p}\bigr)$ using Gauss' Lemma

Published on 26 Mar 2026 - 16:26

99

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Determine if $n$ could be represented by a quadratic form of discriminant $d$

Published on 26 Mar 2026 - 9:49

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When is $-3$ a quadratic residue mod $p$?

Published on 26 Mar 2026 - 9:49

125

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Calculate list of all pairs $(x,y)$

Published on 26 Mar 2026 - 21:25

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For which prime powers are there solutions to $x^{2} + y^{2} = 0 \pmod {p^a}$ with $(x,p) = (y,p) = 1$?

Published on 26 Mar 2026 - 14:34

86

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For any odd prime $p≥5$, $(-3/p) = 1$ if $p ≡ 1,-5\pmod{12}$ and $(-3/p) = -1$ if $p ≡ -1,5 \pmod{12}$

Published on 26 Mar 2026 - 14:35

147

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Finding roots of a polynomial using quadratic reciprocity

Published on 26 Mar 2026 - 14:42

101

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Show for any odd prime $p\geq 5,$ $(-3/p)=1$ or $ -1$

Published on 26 Mar 2026 - 9:49

62

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For each of multiple primes, I choose a particular quadratic residue. Can I always find a square that is not congruent to any of them?

Published on 18 Aug 2020 - 19:59

114

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Find $k$ that will make $a^2-kN=b$ to be divisible by $p_1,p_2...p_s$ for some $a$

Published on 22 Aug 2020 - 2:32

343

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$\sum_{i=0}^k \lfloor\sqrt{ip} \rfloor = \frac{(p^2-1)}{12}$ where p is a prime and $p=4k+1$

Published on 24 Sep 2020 - 10:25

584

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Quadratic residue concept over Elliptic Curves

Published on 30 Sep 2020 - 15:58

68

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Quadratic residues short proof

Published on 06 Oct 2020 - 13:18

143

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Nice lemma regarding factorials and quadratic residues

Published on 26 Mar 2026 - 12:58

List Question

Solving a non-linear congruence

Computing the Legendre symbol $\bigl(\frac{3}{p}\bigr)$ using Gauss' Lemma

Determine if $n$ could be represented by a quadratic form of discriminant $d$

When is $-3$ a quadratic residue mod $p$?

Calculate list of all pairs $(x,y)$

For which prime powers are there solutions to $x^{2} + y^{2} = 0 \pmod {p^a}$ with $(x,p) = (y,p) = 1$?

For any odd prime $p≥5$, $(-3/p) = 1$ if $p ≡ 1,-5\pmod{12}$ and $(-3/p) = -1$ if $p ≡ -1,5 \pmod{12}$

Finding roots of a polynomial using quadratic reciprocity

Show for any odd prime $p\geq 5,$ $(-3/p)=1$ or $ -1$

For each of multiple primes, I choose a particular quadratic residue. Can I always find a square that is not congruent to any of them?

Find $k$ that will make $a^2-kN=b$ to be divisible by $p_1,p_2...p_s$ for some $a$

$\sum_{i=0}^k \lfloor\sqrt{ip} \rfloor = \frac{(p^2-1)}{12}$ where p is a prime and $p=4k+1$

Quadratic residue concept over Elliptic Curves

Quadratic residues short proof

Nice lemma regarding factorials and quadratic residues

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