Question

Let $f(x)=x^3+x^2-5$. Show that for $n=1, 2,3, ...$ there is a unique $x_n$ modulo $7^n$ such that $f(x_n)\equiv 0\pmod{7^n}$.

score 74 · Answer 1 · 2020-02-29 19:51:45

74

Views

Let $f(x)=x^3+x^2-5$. Show that for $n=1, 2,3, ...$ there is a unique $x_n$ modulo $7^n$ such that $f(x_n)\equiv 0\pmod{7^n}$.

Published on 29 Feb 2020 - 19:51

score 1.1k · Answer 2 · 2016-10-19 15:06:43

1.1k

Views

solve x for a cubic congruence equation with large prime mod.

Published on 19 Oct 2016 - 15:06

score 239 · Answer 3 · 2016-11-04 02:17:43

239

Views

rewriting a polynomial congruent to 0 mod m

Published on 04 Nov 2016 - 2:17

score 31 · Answer 4 · 2016-12-05 12:26:58

31

Views

$f \in\mathbb Q[X]$, $ [f] = [f \operatorname{div} X^5] $ in $ \mathbb Q[X]/\equiv_{X^5} $

Published on 05 Dec 2016 - 12:26

score 217 · Answer 5 · 2017-03-18 14:18:58

217

Views

How to solve system of congruences of polynomial?

Published on 18 Mar 2017 - 14:18

score 67 · Answer 6 · 2023-03-27 02:41:19

67

Views

if a homogeneous polynomial is the square of a polynomial modulo $x^2 + y^2 - 1$, is it also congruent to a sum of squares of homogeneous polynomials?

Published on 27 Mar 2023 - 2:41

score 33 · Answer 7 · 2023-05-07 13:33:46

33

Views

Polynomial Congruence Equation

Published on 07 May 2023 - 13:33

score 49 · Answer 8 · 2023-12-23 06:24:00

49

Views

corollary of the partition congruence

Published on 23 Dec 2023 - 6:24

score 64 · Answer 9 · 2024-02-28 14:50:06

64

Views

Is there any prime $p$ such that $6x^3 − p^2 − y^2 = 0$ has an integer solution?

Published on 28 Feb 2024 - 14:50

score 30 · Answer 10 · 2024-03-17 08:20:22

30

Views

The number of solutions to the congruence equation $P(x) \equiv 0 (\mathrm{mod}\ p^\alpha)$

Published on 17 Mar 2024 - 8:20

score 78 · Answer 11 · 2015-03-19 14:01:39

78

Views

Polynomials in Finite Field

Published on 19 Mar 2015 - 14:01

score 549 · Answer 12 · 2015-05-19 08:25:54

549

Views

Solving the congruence $3x^2 + 6x + 1 \equiv 0 \pmod {19}$

Published on 19 May 2015 - 8:25

score 320 · Answer 13 · 2015-06-01 08:45:30

320

Views

Can the concept of congruence be applied to the remainder of a polynomial division?

Published on 01 Jun 2015 - 8:45

score 60 · Answer 14 · 2015-06-10 17:43:43

60

Views

Understanding the following lemma

Published on 10 Jun 2015 - 17:43

score 155 · Answer 15 · 2016-02-25 16:28:31

155

Views

Is there a solution for $x^6 \equiv 5 \pmod {71}$?

Published on 25 Feb 2016 - 16:28

List Question

Let $f(x)=x^3+x^2-5$. Show that for $n=1, 2,3, ...$ there is a unique $x_n$ modulo $7^n$ such that $f(x_n)\equiv 0\pmod{7^n}$.

solve x for a cubic congruence equation with large prime mod.

rewriting a polynomial congruent to 0 mod m

$f \in\mathbb Q[X]$, $ [f] = [f \operatorname{div} X^5] $ in $ \mathbb Q[X]/\equiv_{X^5} $

How to solve system of congruences of polynomial?

if a homogeneous polynomial is the square of a polynomial modulo $x^2 + y^2 - 1$, is it also congruent to a sum of squares of homogeneous polynomials?

Polynomial Congruence Equation

corollary of the partition congruence

Is there any prime $p$ such that $6x^3 − p^2 − y^2 = 0$ has an integer solution?

The number of solutions to the congruence equation $P(x) \equiv 0 (\mathrm{mod}\ p^\alpha)$

Polynomials in Finite Field

Solving the congruence $3x^2 + 6x + 1 \equiv 0 \pmod {19}$

Can the concept of congruence be applied to the remainder of a polynomial division?

Understanding the following lemma

Is there a solution for $x^6 \equiv 5 \pmod {71}$?

Trending Questions

Popular # Hahtags

Popular Questions