Question

If $p$ and $q$ are primes of the form $4k+3$, and $x^2 \equiv p \pmod q$ has no solutions, show $x^2 \equiv q \pmod p$ has two incongruent solutions

score 716 · Answer 1 · 2026-03-26 03:13:27

716

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If $p$ and $q$ are primes of the form $4k+3$, and $x^2 \equiv p \pmod q$ has no solutions, show $x^2 \equiv q \pmod p$ has two incongruent solutions

Published on 26 Mar 2026 - 3:13

score 69 · Answer 2 · 2017-12-10 22:55:28

69

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prove if p is a prime having the form 4k+3

Published on 10 Dec 2017 - 22:55

score 181 · Answer 3 · 2026-03-26 03:11:19

181

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How can we summarize Legendre symbol $(\frac{11}{p})$

Published on 26 Mar 2026 - 3:11

score 55 · Answer 4 · 2026-03-26 06:29:51

55

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Prime factors of $16k^4 +1$ mod $8$

Published on 26 Mar 2026 - 6:29

score 52 · Answer 5 · 2017-12-22 22:53:43

52

Views

irreducible polynomials over GF(q)

Published on 22 Dec 2017 - 22:53

score 930 · Answer 6 · 2018-01-04 23:37:59

930

Views

If N is a quadratic residue modulo p for all primes p<N, is N a perfect square?

Published on 04 Jan 2018 - 23:37

score 131 · Answer 7 · 2018-01-11 15:12:09

131

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Is $u$ a quadratic residue mod $t + nu$?

Published on 11 Jan 2018 - 15:12

score 3.8k · Answer 8 · 2011-04-17 01:07:22

3.8k

Views

Prove that if $p$ is an odd prime that divides a number of the form $n^4 + 1$ then $p \equiv 1 \pmod{8}$

Published on 17 Apr 2011 - 1:07

score 5.5k · Answer 9 · 2011-10-30 23:32:57

5.5k

Views

Find all odd primes $p$ for which $15$ is a quadratic residue modulo $p$

Published on 30 Oct 2011 - 23:32

score 1.5k · Answer 10 · 2011-11-23 15:08:10

1.5k

Views

Elementary proof of when -2 is a quadratic residue modulo an odd prime?

Published on 23 Nov 2011 - 15:08

score 28.6k · Answer 11 · 2012-03-19 12:09:20

28.6k

Views

$-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$

Published on 19 Mar 2012 - 12:09

score 4.9k · Answer 12 · 2026-03-26 17:51:56

4.9k

Views

Legendre symbol, second supplementary law

Published on 26 Mar 2026 - 17:51

score 377 · Answer 13 · 2012-10-28 12:11:07

377

Views

Legendre symbol problem

Published on 28 Oct 2012 - 12:11

score 2.1k · Answer 14 · 2012-11-01 05:02:43

2.1k

Views

Infinitely many primes for quadratic residues

Published on 01 Nov 2012 - 5:02

score 12.6k · Answer 15 · 2026-03-26 08:14:58

12.6k

Views

Determine all primes $p$ for which $5$ is a quadratic residue modulo $p$

Published on 26 Mar 2026 - 8:14

List Question

If $p$ and $q$ are primes of the form $4k+3$, and $x^2 \equiv p \pmod q$ has no solutions, show $x^2 \equiv q \pmod p$ has two incongruent solutions

prove if p is a prime having the form 4k+3

How can we summarize Legendre symbol $(\frac{11}{p})$

Prime factors of $16k^4 +1$ mod $8$

irreducible polynomials over GF(q)

If N is a quadratic residue modulo p for all primes p<N, is N a perfect square?

Is $u$ a quadratic residue mod $t + nu$?

Prove that if $p$ is an odd prime that divides a number of the form $n^4 + 1$ then $p \equiv 1 \pmod{8}$

Find all odd primes $p$ for which $15$ is a quadratic residue modulo $p$

Elementary proof of when -2 is a quadratic residue modulo an odd prime?

$-1$ is a quadratic residue modulo $p$ if and only if $p\equiv 1\pmod{4}$

Legendre symbol, second supplementary law

Legendre symbol problem

Infinitely many primes for quadratic residues

Determine all primes $p$ for which $5$ is a quadratic residue modulo $p$

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