List questions from quadratic-residues

42

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Formula for the root of $x^2=-3\mod n$ when $n=p_1^{k_1}\cdots p_l^{k_l}$ and $p_i$ primes equal to $1\mod 3$

Published on 27 Feb 2021 - 15:22

211

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Why does $a^n \mod p$ always result in a number with Legendre symbol as 1?

Published on 26 Mar 2026 - 17:52

107

Views

Prove that $x^4 \equiv a^2 \pmod p$ is solvable for all $a$

Published on 21 Mar 2021 - 18:32

772

Views

Find all solutions of $x^2 \equiv 9 \pmod{85}$

Published on 22 Mar 2021 - 1:54

55

Views

When is $x$ a square in $\mathbb{F}_p[x]/(Q) $?

Published on 26 Mar 2021 - 13:50

47

Views

Hasse-Minkowski principle and square theorems

Published on 30 Mar 2021 - 11:29

113

Views

Sums of divisors of a Jacobi symbol

Published on 26 Mar 2026 - 11:18

42

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 26 Mar 2026 - 17:53

31

Views

Jacobisymbols modulo $pq$, both prime

Published on 26 Mar 2026 - 17:51

46

Views

Jacobi Quintuple Product Identity

Published on 25 Mar 2026 - 19:01

85

Views

Jacobi Symbol walk through questions

Published on 26 Mar 2026 - 17:53

121

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$p \geq$ 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 26 Mar 2026 - 17:53

86

Views

Divisibility between polynomial expressions

Published on 02 Jun 2021 - 0:14

361

Views

Prove that there are quadratic residues that differ by 6

Published on 26 Mar 2026 - 17:52

75

Views

A doubt in the proof of $\mathbb{Z} + \mathbb{Z}\sqrt m$ is not Euclidean with respect to $\phi_m$

Published on 27 Mar 2026 - 7:35

List Question

Formula for the root of $x^2=-3\mod n$ when $n=p_1^{k_1}\cdots p_l^{k_l}$ and $p_i$ primes equal to $1\mod 3$

Why does $a^n \mod p$ always result in a number with Legendre symbol as 1?

Prove that $x^4 \equiv a^2 \pmod p$ is solvable for all $a$

Find all solutions of $x^2 \equiv 9 \pmod{85}$

When is $x$ a square in $\mathbb{F}_p[x]/(Q) $?

Hasse-Minkowski principle and square theorems

Sums of divisors of a Jacobi symbol

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 $

Jacobisymbols modulo $pq$, both prime

Jacobi Quintuple Product Identity

Jacobi Symbol walk through questions

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

Divisibility between polynomial expressions

Prove that there are quadratic residues that differ by 6

A doubt in the proof of $\mathbb{Z} + \mathbb{Z}\sqrt m$ is not Euclidean with respect to $\phi_m$

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