Question

Jacobi Symbol: $\sum_{n=1}^{p}\left(\sum_{m=1}^{h}\left(\frac{m+n}{p}\right)\right)^2=h(p-h)$

score 263 · Answer 1 · 2026-02-23 04:42:59

263

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Jacobi Symbol: $\sum_{n=1}^{p}\left(\sum_{m=1}^{h}\left(\frac{m+n}{p}\right)\right)^2=h(p-h)$

Published on 23 Feb 2026 - 4:42

score 45 · Answer 2 · 2026-03-25 14:35:54

45

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Prove that $\sum_{a\in\mathbb{Z}/p\mathbb{Z}} (a/p)a^i$ is $0$ if $i\neq (p-1)/2$ and $p-1$ if $i= (p-1)/2$.

Published on 25 Mar 2026 - 14:35

score 57 · Answer 3 · 2026-03-25 09:38:49

57

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A number theory problem: show $N_{x^2−n}(p^k) = 2$ for all $k = 1,2,3,...$

Published on 25 Mar 2026 - 9:38

score 96 · Answer 4 · 2026-03-25 14:32:36

96

Views

Legendre symbol and variable denominator

Published on 25 Mar 2026 - 14:32

score 53 · Answer 5 · 2026-03-25 14:34:42

53

Views

Summations of Legendre Symbols with an odd prime p

Published on 25 Mar 2026 - 14:34

score 38 · Answer 6 · 2026-03-25 14:34:38

38

Views

Computing Legendre symbol of a (p = prime number raised to prime number) mod p?

Published on 25 Mar 2026 - 14:34

score 413 · Answer 7 · 2026-03-25 14:36:50

413

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a) and b) Suppose a = primitive root mod p for an odd prime p. Show that $\left(\frac{a}{p}\right)$ = -1

Published on 25 Mar 2026 - 14:36

score 115 · Answer 8 · 2026-03-25 14:37:59

115

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Primality testing when $n\equiv3\pmod{4}$ and $gcd(totient(n), (n-1)/2) = 1$

Published on 25 Mar 2026 - 14:37

score 449 · Answer 9 · 2026-03-25 14:34:37

449

Views

Legendre symbol sum $\sum\limits_{x=4}^{p-1} \left(\frac{x(1-p-x)}{p}\right)$

Published on 25 Mar 2026 - 14:34

score 614 · Answer 10 · 2026-03-25 14:33:17

614

Views

Show that $x^4 \equiv -4$ (mod $p$) is solvable iff $p \equiv 1$ (mod $4$)

Published on 25 Mar 2026 - 14:33

score 60 · Answer 11 · 2026-03-25 14:37:39

60

Views

Two different outcomes (-1 and 1) for Legendre symbol?

Published on 25 Mar 2026 - 14:37

score 131 · Answer 12 · 2026-03-25 14:36:41

131

Views

Name of group of order $p-\bigl(\frac ap\bigr)$ constructed from field $\Bbb Z_p$?

Published on 25 Mar 2026 - 14:36

score 83 · Answer 13 · 2026-03-25 14:30:46

83

Views

Does $x^4 \equiv -17 \pmod{83}$ has root or not?

Published on 25 Mar 2026 - 14:30

score 54 · Answer 14 · 2026-03-25 14:34:32

54

Views

Cardinality of $ S = \{ x \in \mathbb{Z}_p^* | \phi(1-x^2) = 1 \}$

Published on 25 Mar 2026 - 14:34

score 884 · Answer 15 · 2026-03-25 14:34:34

884

Views

Sum of Legendre symbols is 0?

Published on 25 Mar 2026 - 14:34

List Question

Jacobi Symbol: $\sum_{n=1}^{p}\left(\sum_{m=1}^{h}\left(\frac{m+n}{p}\right)\right)^2=h(p-h)$

Prove that $\sum_{a\in\mathbb{Z}/p\mathbb{Z}} (a/p)a^i$ is $0$ if $i\neq (p-1)/2$ and $p-1$ if $i= (p-1)/2$.

A number theory problem: show $N_{x^2−n}(p^k) = 2$ for all $k = 1,2,3,...$

Legendre symbol and variable denominator

Summations of Legendre Symbols with an odd prime p

Computing Legendre symbol of a (p = prime number raised to prime number) mod p?

a) and b) Suppose a = primitive root mod p for an odd prime p. Show that $\left(\frac{a}{p}\right)$ = -1

Primality testing when $n\equiv3\pmod{4}$ and $gcd(totient(n), (n-1)/2) = 1$

Legendre symbol sum $\sum\limits_{x=4}^{p-1} \left(\frac{x(1-p-x)}{p}\right)$

Show that $x^4 \equiv -4$ (mod $p$) is solvable iff $p \equiv 1$ (mod $4$)

Two different outcomes (-1 and 1) for Legendre symbol?

Name of group of order $p-\bigl(\frac ap\bigr)$ constructed from field $\Bbb Z_p$?

Does $x^4 \equiv -17 \pmod{83}$ has root or not?

Cardinality of $ S = \{ x \in \mathbb{Z}_p^* | \phi(1-x^2) = 1 \}$

Sum of Legendre symbols is 0?

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