Question

Why is $\left( \frac {a}{p} \right)= 1$ equivalent to $p$ satisfying some condition mod $4a$, for odd prime $p$?

score 70 · Answer 1 · 2026-03-26 17:53:16

70

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Why is $\left( \frac {a}{p} \right)= 1$ equivalent to $p$ satisfying some condition mod $4a$, for odd prime $p$?

Published on 26 Mar 2026 - 17:53

score 324 · Answer 2 · 2026-03-25 15:59:19

324

Views

Perfect squares and cubes in quadratic number fields

Published on 25 Mar 2026 - 15:59

score 244 · Answer 3 · 2021-07-08 14:29:38

244

Views

An exercise in "Number Theory" by Shafarevich and Borevich

Published on 08 Jul 2021 - 14:29

score 48 · Answer 4 · 2021-07-08 15:26:48

48

Views

Showing $\sum_{m=1}^{q-1}m^{(q+1)/2}\equiv0\bmod{q}$, where $q$ is an odd prime congruent to $3 \bmod{4}$

Published on 08 Jul 2021 - 15:26

score 96 · Answer 5 · 2026-03-26 17:52:53

96

Views

Question about Legendre Symbol and Division Q12(a)

Published on 26 Mar 2026 - 17:52

score 87 · Answer 6 · 2021-07-23 18:23:01

87

Views

What is the most complete binary quadratic form table?

Published on 23 Jul 2021 - 18:23

score 323 · Answer 7 · 2021-07-28 09:40:16

323

Views

Quadratic residue test for mod powers of 2

Published on 28 Jul 2021 - 9:40

score 95 · Answer 8 · 2021-08-01 15:58:22

95

Views

Proving that if prime p>3 divides a^2 + 12, then p is congruent 2(mod 3)

Published on 01 Aug 2021 - 15:58

score 40 · Answer 9 · 2021-08-15 18:03:51

40

Views

$a^2 \equiv kb^2 \pmod p$ implies solution to $x^2 \equiv k \pmod p$

Published on 15 Aug 2021 - 18:03

score 147 · Answer 10 · 2021-09-01 17:07:10

147

Views

Is $62$ a quadratic residue module $187$?

Published on 01 Sep 2021 - 17:07

score 72 · Answer 11 · 2021-09-13 11:29:08

72

Views

Find the sum of all primes less than $75$ that can be factors of $n^2-3$ such that $n≥2$

Published on 13 Sep 2021 - 11:29

score 163 · Answer 12 · 2021-10-13 15:43:15

163

Views

Counting solutions to $x^2+y^2 \equiv d \pmod{p}$ for a prime $p \equiv 3 \pmod 4$

Published on 13 Oct 2021 - 15:43

score 123 · Answer 13 · 2021-10-21 22:57:38

123

Views

Generalization of Quadratic Residues to other rings?

Published on 21 Oct 2021 - 22:57

score 66 · Answer 14 · 2021-10-22 01:35:11

66

Views

Is factoring primes $pq$ eqivalent to discovering $p+q$, thus binding $q$ and the search for $(p+q)$ when $(q/p) < 4$?

Published on 22 Oct 2021 - 1:35

score 31 · Answer 15 · 2021-10-22 20:15:19

31

Views

Correctness of $\sigma_s(n) (1-\frac{1}{n^s}) = 0 \pmod{k}$ (divisor sum congruence)

Published on 22 Oct 2021 - 20:15

List Question

Why is $\left( \frac {a}{p} \right)= 1$ equivalent to $p$ satisfying some condition mod $4a$, for odd prime $p$?

Perfect squares and cubes in quadratic number fields

An exercise in "Number Theory" by Shafarevich and Borevich

Showing $\sum_{m=1}^{q-1}m^{(q+1)/2}\equiv0\bmod{q}$, where $q$ is an odd prime congruent to $3 \bmod{4}$

Question about Legendre Symbol and Division Q12(a)

What is the most complete binary quadratic form table?

Quadratic residue test for mod powers of 2

Proving that if prime p>3 divides a^2 + 12, then p is congruent 2(mod 3)

$a^2 \equiv kb^2 \pmod p$ implies solution to $x^2 \equiv k \pmod p$

Is $62$ a quadratic residue module $187$?

Find the sum of all primes less than $75$ that can be factors of $n^2-3$ such that $n≥2$

Counting solutions to $x^2+y^2 \equiv d \pmod{p}$ for a prime $p \equiv 3 \pmod 4$

Generalization of Quadratic Residues to other rings?

Is factoring primes $pq$ eqivalent to discovering $p+q$, thus binding $q$ and the search for $(p+q)$ when $(q/p) < 4$?

Correctness of $\sigma_s(n) (1-\frac{1}{n^s}) = 0 \pmod{k}$ (divisor sum congruence)

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