Question

How can I construct polynomials with "small" coefficients generating a prime "late"?

score 247 · Answer 1 · 2026-03-25 05:00:05

247

Views

How can I construct polynomials with "small" coefficients generating a prime "late"?

Published on 25 Mar 2026 - 5:00

score 74 · Answer 2 · 2026-03-25 04:18:50

74

Views

Fixed points of a homogeneous polynomial

Published on 25 Mar 2026 - 4:18

score 66 · Answer 3 · 2026-03-25 11:31:41

66

Views

Proof using concept of polynomials.

Published on 25 Mar 2026 - 11:31

score 109 · Answer 4 · 2026-03-29 22:33:12

109

Views

Show that $\dfrac{b}{a} = -(A+B+C)$ and $\dfrac{c}{a} = (AB+AC + BC)$

Published on 29 Mar 2026 - 22:33

score 1.9k · Answer 5 · 2026-03-25 22:30:52

1.9k

Views

Show that $\Bbb F_2[x]/(x^3+x+1)$ is a field and more...

Published on 25 Mar 2026 - 22:30

score 93 · Answer 6 · 2018-03-30 10:57:46

Here is a problem based on polynomials and I'm not being able to understand how to proceed. Could anyone solve it? Many thanks?

score 116 · Answer 7 · 2026-03-29 10:02:11

116

Views

Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$

Published on 29 Mar 2026 - 10:02

score 30 · Answer 8 · 2026-03-25 11:32:59

30

Views

Proof that if polynomial in $\mathbb{Z}[x]$ has a rational root $a/b$ and $k$ is an integer, then $a-kb|f(k)$.

Published on 25 Mar 2026 - 11:32

score 60 · Answer 9 · 2026-03-27 07:11:52

60

Views

Vector space polynomials

Published on 27 Mar 2026 - 7:11

score 82 · Answer 10 · 2026-03-29 22:33:48

82

Views

Prove that if the roots of the polynomial $x^2+ ax+ b + 1 $ are positive integers, then a and b are integers.

Published on 29 Mar 2026 - 22:33

score 815 · Answer 11 · 2026-03-25 09:23:01

815

Views

Solving x^4 - 1 ≡ 0 MOD (55)

Published on 25 Mar 2026 - 9:23

score 158 · Answer 12 · 2026-03-26 01:12:38

158

Views

Given three positive numbers $x,y,z$. Prove that $(x+y-z)(\frac{3}{x+y}-\frac{1}{y+z}-\frac{1}{z+x})\leqq\frac{1}{2}$ .

Published on 26 Mar 2026 - 1:12

score 157 · Answer 13 · 2026-03-25 09:50:52

157

Views

A determinant involving a polynomial is $0$

Published on 25 Mar 2026 - 9:50

score 126 · Answer 14 · 2026-03-22 20:19:01

126

Views

Which family of orthogonal polynomials satisfies these conditions?

Published on 22 Mar 2026 - 20:19

score 86 · Answer 15 · 2018-03-31 14:12:07

86

Views

Solving for $x$ from given equation

Published on 31 Mar 2018 - 14:12

List Question

How can I construct polynomials with "small" coefficients generating a prime "late"?

Fixed points of a homogeneous polynomial

Proof using concept of polynomials.

Show that $\dfrac{b}{a} = -(A+B+C)$ and $\dfrac{c}{a} = (AB+AC + BC)$

Show that $\Bbb F_2[x]/(x^3+x+1)$ is a field and more...

Here is a problem based on polynomials and I'm not being able to understand how to proceed. Could anyone solve it? Many thanks?

Prove $Σ_{cyc}\frac{1}{\left(a+1\right)^2}+\frac{1}{a+b+c+1}\ge 1$

Proof that if polynomial in $\mathbb{Z}[x]$ has a rational root $a/b$ and $k$ is an integer, then $a-kb|f(k)$.

Vector space polynomials

Prove that if the roots of the polynomial $x^2+ ax+ b + 1 $ are positive integers, then a and b are integers.

Solving x^4 - 1 ≡ 0 MOD (55)

Given three positive numbers $x,y,z$. Prove that $(x+y-z)(\frac{3}{x+y}-\frac{1}{y+z}-\frac{1}{z+x})\leqq\frac{1}{2}$ .

A determinant involving a polynomial is $0$

Which family of orthogonal polynomials satisfies these conditions?

Solving for $x$ from given equation

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