Question

Why does the cube root of a polynomial in a finite field produce a different polynomial when re-cubed?

score 651 · Answer 1 · 2026-05-02 18:41:25

651

Views

Why does the cube root of a polynomial in a finite field produce a different polynomial when re-cubed?

Published on 02 May 2026 - 18:41

score 74 · Answer 2 · 2026-04-16 01:42:45

74

Views

$deg(P) = 4$, then $P'$ doesn't have all zeros real if $P$ has 2 complex zeros and 2 real zeros

Published on 16 Apr 2026 - 1:42

score 81 · Answer 3 · 2026-04-09 04:48:21

81

Views

Simplify sqrt-Inequality to prove monotonicity of a series

Published on 09 Apr 2026 - 4:48

score 1.5k · Answer 4 · 2026-05-13 02:33:04

1.5k

Views

An $n$ degree polynomial with more than $n$ roots?

Published on 13 May 2026 - 2:33

score 200 · Answer 5 · 2026-04-13 15:47:10

200

Views

An Elliptic Curve Question

Published on 13 Apr 2026 - 15:47

score 251 · Answer 6 · 2026-04-11 09:33:26

251

Views

Are positive Vieta's equations sufficient for negative roots?

Published on 11 Apr 2026 - 9:33

score 66 · Answer 7 · 2026-05-11 22:27:10

66

Views

Numerical analysis: Chebyshev coefficient representation error.

Published on 11 May 2026 - 22:27

score 262 · Answer 8 · 2026-04-14 17:36:15

262

Views

Let $a$ be the real root of the equation $x^3+x+1=0$

Published on 14 Apr 2026 - 17:36

score 208 · Answer 9 · 2026-04-09 08:40:47

208

Views

Can numerical methods be used to prove a root does NOT exist?

Published on 09 Apr 2026 - 8:40

score 80 · Answer 10 · 2026-05-10 13:49:05

80

Views

Fixed points of a homogeneous polynomial

Published on 10 May 2026 - 13:49

score 110 · Answer 11 · 2026-04-15 10:51:34

110

Views

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

Published on 15 Apr 2026 - 10:51

score 33 · Answer 12 · 2026-05-11 05:25:36

33

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 11 May 2026 - 5:25

score 83 · Answer 13 · 2026-04-14 19:39:27

83

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 14 Apr 2026 - 19:39

score 22 · Answer 14 · 2026-05-11 05:33:47

22

Views

Roots of a composition of functions where the inner function has a quotient space as its range

Published on 11 May 2026 - 5:33

score 2k · Answer 15 · 2026-05-10 16:13:57

2k

Views

What is the intuition for the multiplicity of a root of a polynomial equation?

Published on 10 May 2026 - 16:13

List Question

Why does the cube root of a polynomial in a finite field produce a different polynomial when re-cubed?

$deg(P) = 4$, then $P'$ doesn't have all zeros real if $P$ has 2 complex zeros and 2 real zeros

Simplify sqrt-Inequality to prove monotonicity of a series

An $n$ degree polynomial with more than $n$ roots?

An Elliptic Curve Question

Are positive Vieta's equations sufficient for negative roots?

Numerical analysis: Chebyshev coefficient representation error.

Let $a$ be the real root of the equation $x^3+x+1=0$

Can numerical methods be used to prove a root does NOT exist?

Fixed points of a homogeneous polynomial

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

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

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

Roots of a composition of functions where the inner function has a quotient space as its range

What is the intuition for the multiplicity of a root of a polynomial equation?

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