Question

Proof problem : show that $\frac{n_{1}n_{2}-1}{2}$ = $\frac{n_{1}-1}{2}$ + $\frac{n_{2}-1}{2}$ mod(2)

score 47 · Answer 1 · 2017-12-21 19:10:55

47

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Proof problem : show that $\frac{n_{1}n_{2}-1}{2}$ = $\frac{n_{1}-1}{2}$ + $\frac{n_{2}-1}{2}$ mod(2)

Published on 21 Dec 2017 - 19:10

score 119 · Answer 2 · 2017-12-26 16:31:10

119

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Evaluating $\left(\frac{-2}{p}\right)$

Published on 26 Dec 2017 - 16:31

score 1.5k · Answer 3 · 2011-03-10 16:35:06

1.5k

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Legendre symbol: Showing that $\sum_{m=0}^{p-1} \left(\frac{am+b}{p}\right)=0$

Published on 10 Mar 2011 - 16:35

score 999 · Answer 4 · 2012-05-23 15:32:00

999

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Describing the primes $p$ for which the Legendre symbol $(\frac{-6}{p})=1$

Published on 23 May 2012 - 15:32

score 4.9k · Answer 5 · 2012-08-07 16:44:11

4.9k

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Legendre symbol, second supplementary law

Published on 07 Aug 2012 - 16:44

score 2.9k · Answer 6 · 2013-03-18 11:43:59

2.9k

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sum of the product of consecutive legendre symbols is -1

Published on 18 Mar 2013 - 11:43

score 2.1k · Answer 7 · 2013-03-25 22:33:48

2.1k

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How can I prove these summations for the legendre symbol

Published on 25 Mar 2013 - 22:33

score 1.6k · Answer 8 · 2013-03-27 02:48:27

1.6k

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

Published on 27 Mar 2013 - 2:48

score 1.9k · Answer 9 · 2013-03-27 10:56:09

1.9k

Views

Proof involving Legendre Symbol: $\left(\frac{3}{p}\right) = 1$ iff $p \equiv \pm 1 \pmod{12}$

Published on 27 Mar 2013 - 10:56

score 245 · Answer 10 · 2020-08-12 05:08:27

245

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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 12 Aug 2020 - 5:08

score 85 · Answer 11 · 2020-08-17 02:31:45

85

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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 17 Aug 2020 - 2:31

score 101 · Answer 12 · 2026-03-26 09:49:54

101

Views

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

Published on 26 Mar 2026 - 9:49

score 415 · Answer 13 · 2020-09-14 16:50:21

415

Views

Legendre symbol for (2/p)

Published on 14 Sep 2020 - 16:50

score 48 · Answer 14 · 2020-09-23 16:46:45

48

Views

Show that the following function is a homomorphism.

Published on 23 Sep 2020 - 16:46

score 64 · Answer 15 · 2020-10-12 08:27:01

64

Views

For odd prime $p$, show there exist nonzero residues $x$ and $y$ mod $p$ s.t. $ax^2+by^2 \equiv 0$ mod $p$ iff $(\frac{-ab}{p}) = 1$

Published on 12 Oct 2020 - 8:27

List Question

Proof problem : show that $\frac{n_{1}n_{2}-1}{2}$ = $\frac{n_{1}-1}{2}$ + $\frac{n_{2}-1}{2}$ mod(2)

Evaluating $\left(\frac{-2}{p}\right)$

Legendre symbol: Showing that $\sum_{m=0}^{p-1} \left(\frac{am+b}{p}\right)=0$

Describing the primes $p$ for which the Legendre symbol $(\frac{-6}{p})=1$

Legendre symbol, second supplementary law

sum of the product of consecutive legendre symbols is -1

How can I prove these summations for the legendre symbol

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

Proof involving Legendre Symbol: $\left(\frac{3}{p}\right) = 1$ iff $p \equiv \pm 1 \pmod{12}$

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 $p ≡ -1,5 \pmod{12}$

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

Legendre symbol for (2/p)

Show that the following function is a homomorphism.

For odd prime $p$, show there exist nonzero residues $x$ and $y$ mod $p$ s.t. $ax^2+by^2 \equiv 0$ mod $p$ iff $(\frac{-ab}{p}) = 1$

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