Question

If the congruence $ x^2 \equiv n \bmod{P} $ has a solution then $(n \mid p_i) = 1 $ for each prime $ p_i $ that divides $ P $

score 41 · Answer 1 · 2021-04-10 17:04:14

41

Views

If the congruence $ x^2 \equiv n \bmod{P} $ has a solution then $(n \mid p_i) = 1 $ for each prime $ p_i $ that divides $ P $

Published on 10 Apr 2021 - 17:04

score 43 · Answer 2 · 2021-04-14 11:26:15

43

Views

Why does $p \nmid m$ imply $\left(\frac{-4m^2} p\right) = \left(\frac{-1 } p\right)$?

Published on 14 Apr 2021 - 11:26

score 30 · Answer 3 · 2021-04-17 09:31:13

30

Views

Jacobisymbols modulo $pq$, both prime

Published on 17 Apr 2021 - 9:31

score 66 · Answer 4 · 2021-04-24 17:52:44

66

Views

Class number of positive definite binary quadratic forms formula

Published on 24 Apr 2021 - 17:52

score 60 · Answer 5 · 2021-05-16 11:35:42

60

Views

Show that $2a \equiv -(-1)^m {2m \choose m} \pmod{p}$ where $m={p-1 \over 4}$

Published on 16 May 2021 - 11:35

score 84 · Answer 6 · 2021-05-18 00:01:37

84

Views

Jacobi Symbol walk through questions

Published on 18 May 2021 - 0:01

score 120 · Answer 7 · 2021-05-21 19:54:01

120

Views

For a fixed $a$, can we say $\left[\frac{a}{p}\right]_q=-1$ for infinitely many $p$?

Published on 21 May 2021 - 19:54

score 120 · Answer 8 · 2021-05-27 15:41:55

120

Views

$p \geq$ 7 show $\Big( \frac{n}{p} \Big)=\Big( \frac{n+1}{p} \Big) =1$ for atleast one n in the set $\{ 1,2,\ldots,,9 \}$

Published on 27 May 2021 - 15:41

score 124 · Answer 9 · 2021-05-31 08:52:53

124

Views

definite integral solution for $\int^{\pi}_{\alpha} P_{n}(\cos\theta)\:P_{m}(\cos\theta)\sin\theta\:d\theta$

Published on 31 May 2021 - 8:52

score 96 · Answer 10 · 2021-06-05 12:13:44

96

Views

Legendre symbol in the Fibonacci primality test

Published on 05 Jun 2021 - 12:13

score 360 · Answer 11 · 2021-06-08 15:46:18

360

Views

Prove that there are quadratic residues that differ by 6

Published on 08 Jun 2021 - 15:46

score 102 · Answer 12 · 2021-06-10 08:03:06

102

Views

Show that $p\equiv 3\pmod 4$ being prime implies $x^2+y^2\equiv n\pmod p$ has $p+1$ solutions

Published on 10 Jun 2021 - 8:03

score 69 · Answer 13 · 2021-06-16 11:20:53

69

Views

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

Published on 16 Jun 2021 - 11:20

score 95 · Answer 14 · 2021-07-17 10:21:52

95

Views

Question about Legendre Symbol and Division Q12(a)

Published on 17 Jul 2021 - 10:21

score 76 · Answer 15 · 2026-03-25 19:25:29

76

Views

Only Legendre symbol gives constant magnitude discrete Fourier transform

Published on 25 Mar 2026 - 19:25

List Question

If the congruence $ x^2 \equiv n \bmod{P} $ has a solution then $(n \mid p_i) = 1 $ for each prime $ p_i $ that divides $ P $

Why does $p \nmid m$ imply $\left(\frac{-4m^2} p\right) = \left(\frac{-1 } p\right)$?

Jacobisymbols modulo $pq$, both prime

Class number of positive definite binary quadratic forms formula

Show that $2a \equiv -(-1)^m {2m \choose m} \pmod{p}$ where $m={p-1 \over 4}$

Jacobi Symbol walk through questions

For a fixed $a$, can we say $\left[\frac{a}{p}\right]_q=-1$ for infinitely many $p$?

$p \geq$ 7 show $\Big( \frac{n}{p} \Big)=\Big( \frac{n+1}{p} \Big) =1$ for atleast one n in the set $\{ 1,2,\ldots,,9 \}$

definite integral solution for $\int^{\pi}_{\alpha} P_{n}(\cos\theta)\:P_{m}(\cos\theta)\sin\theta\:d\theta$

Legendre symbol in the Fibonacci primality test

Prove that there are quadratic residues that differ by 6

Show that $p\equiv 3\pmod 4$ being prime implies $x^2+y^2\equiv n\pmod p$ has $p+1$ solutions

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

Question about Legendre Symbol and Division Q12(a)

Only Legendre symbol gives constant magnitude discrete Fourier transform

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