Question

Prove that there are $p+1$ points on the elliptic curve $y^2 = x^3 + 1$ over $\mathbb{F}_p$, where $p > 3$ is a prime such that $p \equiv 2 \pmod 3$.

score 1.6k · Answer 1 · 2026-04-16 01:27:27

1.6k

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Prove that there are $p+1$ points on the elliptic curve $y^2 = x^3 + 1$ over $\mathbb{F}_p$, where $p > 3$ is a prime such that $p \equiv 2 \pmod 3$.

Published on 16 Apr 2026 - 1:27

score 307 · Answer 2 · 2026-04-14 00:20:54

307

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Problem related polynomial ring over finite field of intergers

Published on 14 Apr 2026 - 0:20

score 242 · Answer 3 · 2026-04-12 11:00:13

242

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Group does not contain any elements of order $p^2$?

Published on 12 Apr 2026 - 11:00

score 213 · Answer 4 · 2026-04-15 17:15:14

213

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Irreducible polynomials over $F_q$ with exponents of the form $q^k - 1$.

Published on 15 Apr 2026 - 17:15

score 181 · Answer 5 · 2026-04-11 07:43:45

181

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System of equation over GF(211) (corrected)

Published on 11 Apr 2026 - 7:43

score 621 · Answer 6 · 2026-04-08 19:32:51

621

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Field construction

Published on 08 Apr 2026 - 19:32

score 247 · Answer 7 · 2026-04-17 14:48:38

247

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Show the polynomial $(x-\alpha)(x-\alpha^p)\cdots(x-\alpha^{p^{n-1}})$ is in $F_p[x]$ if $\alpha\in F_{p^n}$

Published on 17 Apr 2026 - 14:48

score 909 · Answer 8 · 2026-04-13 08:47:08

909

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Nonzero trace in finite fields and proving irreducibility.

Published on 13 Apr 2026 - 8:47

score 2.9k · Answer 9 · 2026-04-08 14:35:50

2.9k

Views

arithmetic operations in Galois Field

Published on 08 Apr 2026 - 14:35

score 82 · Answer 10 · 2026-04-09 14:52:42

82

Views

why using irriducible polinomial for galois field?

Published on 09 Apr 2026 - 14:52

score 157 · Answer 11 · 2026-04-13 16:02:34

157

Views

Using characters in finite fields to find number of solutions to polynomials.

Published on 13 Apr 2026 - 16:02

score 2.7k · Answer 12 · 2026-04-28 12:19:47

2.7k

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Quadratic Extension of Finite field

Published on 28 Apr 2026 - 12:19

score 974 · Answer 13 · 2026-04-14 00:44:13

974

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Generators of Finite Fields and Quadratic Extensions

Published on 14 Apr 2026 - 0:44

score 215 · Answer 14 · 2026-04-10 11:33:31

215

Views

Is the modular multiplicative inverse of $a$ equal to that of $-a$?

Published on 10 Apr 2026 - 11:33

score 1k · Answer 15 · 2026-04-17 03:27:09

1k

Views

Isomorphism for optimization of GF256 implementation in AES S-Box using intermediary finite fields

Published on 17 Apr 2026 - 3:27

List Question

Prove that there are $p+1$ points on the elliptic curve $y^2 = x^3 + 1$ over $\mathbb{F}_p$, where $p > 3$ is a prime such that $p \equiv 2 \pmod 3$.

Problem related polynomial ring over finite field of intergers

Group does not contain any elements of order $p^2$?

Irreducible polynomials over $F_q$ with exponents of the form $q^k - 1$.

System of equation over GF(211) (corrected)

Field construction

Show the polynomial $(x-\alpha)(x-\alpha^p)\cdots(x-\alpha^{p^{n-1}})$ is in $F_p[x]$ if $\alpha\in F_{p^n}$

Nonzero trace in finite fields and proving irreducibility.

arithmetic operations in Galois Field

why using irriducible polinomial for galois field?

Using characters in finite fields to find number of solutions to polynomials.

Quadratic Extension of Finite field

Generators of Finite Fields and Quadratic Extensions

Is the modular multiplicative inverse of $a$ equal to that of $-a$?

Isomorphism for optimization of GF256 implementation in AES S-Box using intermediary finite fields

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