List questions from quadratic-reciprocity

Published on 15 Mar 2013 - 9:35

139

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Prove of Quadratic residual

Published on 20 Mar 2013 - 15:20

2.1k

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When computing the Legendre symbol $(\frac{3}{p})$, how to combine different congruences together into one statement?

Published on 28 Mar 2013 - 17:04

499

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Probability that $x \equiv 3 \pmod{4}$

Published on 30 Mar 2013 - 19:21

111

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Showing that if $p_1\equiv p_2 \pmod{4n}$, then $(\frac{n}{p_1})=(\frac{n}{p2})$

Published on 30 Mar 2013 - 23:00

98

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

Published on 31 Jul 2020 - 15:45

53

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Are $3$ and $19$ the only primes representable by the principal form with discriminant $-57$?

Published on 31 Jul 2020 - 18:59

1.5k

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

Published on 01 Aug 2020 - 3:00

192

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If $p\equiv 1 \;\text{mod}\; 3$, then show that one can find an integer $k$ satisfying $k^2-k+1=p\cdot M\;$ with $M<p$

Published on 12 Aug 2020 - 6:22

146

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Finding roots of a polynomial using quadratic reciprocity

Published on 17 Aug 2020 - 18:33

100

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

Published on 18 Aug 2020 - 3:36

138

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Let $p=40k+9$ be prime. Does $10$ always have even order mod $p$?

Published on 23 Feb 2026 - 16:58

168

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Law of Quadratic Reciprocity for primes that are congruent 3 or 1 modulo 4

Published on 25 Sep 2020 - 18:26

142

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Nice lemma regarding factorials and quadratic residues

Published on 09 Oct 2020 - 8:07

166

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Integers that are square modulo all powers of 2

Published on 12 Oct 2020 - 21:08

List Question

If $p \equiv 1 \mod{4}$ is prime, how to find a quadratic nonresidue modulo $p$?

Prove of Quadratic residual

When computing the Legendre symbol $(\frac{3}{p})$, how to combine different congruences together into one statement?

Probability that $x \equiv 3 \pmod{4}$

Showing that if $p_1\equiv p_2 \pmod{4n}$, then $(\frac{n}{p_1})=(\frac{n}{p2})$

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

Are $3$ and $19$ the only primes representable by the principal form with discriminant $-57$?

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

If $p\equiv 1 \;\text{mod}\; 3$, then show that one can find an integer $k$ satisfying $k^2-k+1=p\cdot M\;$ with $M<p$

Finding roots of a polynomial using quadratic reciprocity

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

Let $p=40k+9$ be prime. Does $10$ always have even order mod $p$?

Law of Quadratic Reciprocity for primes that are congruent 3 or 1 modulo 4

Nice lemma regarding factorials and quadratic residues

Integers that are square modulo all powers of 2

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