Question

Find a prime number p that is simultaneously expressible in the forms:

score 218 · Answer 1 · 2015-10-01 22:03:17

218

Views

Find a prime number p that is simultaneously expressible in the forms:

Published on 01 Oct 2015 - 22:03

score 151 · Answer 2 · 2015-10-02 01:39:58

151

Views

Legendre Symbol, $(\frac{a}{p})=(\frac{a+1}{p})=1$

Published on 02 Oct 2015 - 1:39

score 986 · Answer 3 · 2026-03-16 03:20:40

986

Views

Cryptography: Solve $x^2 \equiv 331 \pmod{385}$ using modular arithmetic

Published on 16 Mar 2026 - 3:20

score 116 · Answer 4 · 2015-10-26 05:51:22

116

Views

Why does the Legendre symbol $(\frac {p}{3}) = 1 $ if $p \equiv 1 \pmod 3$ and $-1$ if $p \equiv 2 \pmod 3$?

Published on 26 Oct 2015 - 5:51

score 359 · Answer 5 · 2015-10-27 06:32:30

359

Views

If $n\in\Bbb Z^+$ is not a square, prove exist infinitely many primes $p$ such that $\left(\frac{n}{p}\right)=-1$.

Published on 27 Oct 2015 - 6:32

score 116 · Answer 6 · 2015-10-27 21:47:35

116

Views

Prove that a quadratic equation has no roots in a congruence class

Published on 27 Oct 2015 - 21:47

score 186 · Answer 7 · 2026-03-09 15:02:30

186

Views

Prove that there are no solutions to $x^2 + x + 1 \equiv 0$ (mod $n$) in $\mathbb{Z}/_{n}\mathbb{Z}$

Published on 09 Mar 2026 - 15:02

score 2.2k · Answer 8 · 2015-10-28 14:22:44

2.2k

Views

Legendre symbol $(-3/p)$ where $p = 1 \mod 3$

Published on 28 Oct 2015 - 14:22

score 963 · Answer 9 · 2026-03-25 09:06:32

963

Views

Jacobi's Symbol

Published on 25 Mar 2026 - 9:06

score 103 · Answer 10 · 2026-03-21 12:49:19

103

Views

Infinite graph with Legendre symbol .

Published on 21 Mar 2026 - 12:49

score 1.3k · Answer 11 · 2015-11-15 17:30:20

1.3k

Views

Sum of Legendre symbols: $\sum _{n=1}^p \left(\frac{an+b}{p}\right)=0$

Published on 15 Nov 2015 - 17:30

score 147 · Answer 12 · 2026-03-24 15:52:42

147

Views

Use that $ (\mathbb{Z}/p\mathbb{Z})^{*} $ is cyclic to give a direct proof that $ \left( \frac{-3}{p} \right) = 1 $ when $ p \equiv 1\ (\bmod\ 3) $.

Published on 24 Mar 2026 - 15:52

score 108 · Answer 13 · 2015-11-19 22:29:06

108

Views

Showing $x(2x - 1)$ is a Fermat pseudoprime given $x$ is odd prime and other conditions

Published on 19 Nov 2015 - 22:29

score 543 · Answer 14 · 2015-11-20 21:03:57

543

Views

Proving 2047 is not an euler pseudoprime

Published on 20 Nov 2015 - 21:03

score 418 · Answer 15 · 2015-12-07 23:26:50

418

Views

Number Theory: Find $m\equiv 1\pmod4$ so that $x^2\equiv -1\pmod{m}$ has no solution.

Published on 07 Dec 2015 - 23:26

List Question

Find a prime number p that is simultaneously expressible in the forms:

Legendre Symbol, $(\frac{a}{p})=(\frac{a+1}{p})=1$

Cryptography: Solve $x^2 \equiv 331 \pmod{385}$ using modular arithmetic

Why does the Legendre symbol $(\frac {p}{3}) = 1 $ if $p \equiv 1 \pmod 3$ and $-1$ if $p \equiv 2 \pmod 3$?

If $n\in\Bbb Z^+$ is not a square, prove exist infinitely many primes $p$ such that $\left(\frac{n}{p}\right)=-1$.

Prove that a quadratic equation has no roots in a congruence class

Prove that there are no solutions to $x^2 + x + 1 \equiv 0$ (mod $n$) in $\mathbb{Z}/_{n}\mathbb{Z}$

Legendre symbol $(-3/p)$ where $p = 1 \mod 3$

Jacobi's Symbol

Infinite graph with Legendre symbol .

Sum of Legendre symbols: $\sum _{n=1}^p \left(\frac{an+b}{p}\right)=0$

Use that $ (\mathbb{Z}/p\mathbb{Z})^{*} $ is cyclic to give a direct proof that $ \left( \frac{-3}{p} \right) = 1 $ when $ p \equiv 1\ (\bmod\ 3) $.

Showing $x(2x - 1)$ is a Fermat pseudoprime given $x$ is odd prime and other conditions

Proving 2047 is not an euler pseudoprime

Number Theory: Find $m\equiv 1\pmod4$ so that $x^2\equiv -1\pmod{m}$ has no solution.

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