Question

What sufficient criteria are there for a polynomial to be separable?

score 54 · Answer 1 · 2026-04-09 08:10:47

54

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What sufficient criteria are there for a polynomial to be separable?

Published on 09 Apr 2026 - 8:10

score 979 · Answer 2 · 2026-04-17 20:31:30

979

Views

Show that $x^{p^m} - x$ divides $x^{p^n} - x$ if and only if $m$ divides $n$.

Published on 17 Apr 2026 - 20:31

score 75 · Answer 3 · 2026-04-16 12:56:49

75

Views

Polynomials vector space and direct sums

Published on 16 Apr 2026 - 12:56

score 607 · Answer 4 · 2026-04-15 21:08:39

607

Views

Prove that if $f(x)$ divides $g(x)$ and $f(x)$ divides $h(x)$, then $f(x)$ divides $s(x)g(x) +t(x)h(x)$.

Published on 15 Apr 2026 - 21:08

score 157 · Answer 5 · 2026-04-15 21:40:07

157

Views

How do you prove that $\binom{n}{d} = \Theta(n^d)$?

Published on 15 Apr 2026 - 21:40

score 37 · Answer 6 · 2026-04-11 00:39:09

37

Views

characteristic polynomial with rows as coordinates

Published on 11 Apr 2026 - 0:39

score 10.7k · Answer 7 · 2026-04-16 10:12:52

10.7k

Views

Why is 1, x and $x^2$ linearly independent?

Published on 16 Apr 2026 - 10:12

score 390 · Answer 8 · 2026-04-10 01:24:11

390

Views

Is it true that no polynomial (with the exception of constant polynomial) have an inverse in $\mathbb Z/p\mathbb Z$ (where p is prime)?

Published on 10 Apr 2026 - 1:24

score 53 · Answer 9 · 2026-04-13 11:56:09

53

Views

Proving the mean zero condition for polynomials over finite fields by linear algebra

Published on 13 Apr 2026 - 11:56

score 1.5k · Answer 10 · 2026-04-16 06:18:16

1.5k

Views

Finding values for K such that the roots of the quadratic are strictly imaginary: $x^2+\left(K^2+3K-7\right)x+K$

Published on 16 Apr 2026 - 6:18

score 35 · Answer 11 · 2026-04-08 19:34:31

35

Views

Finding factors of polynomials without every power descending

Published on 08 Apr 2026 - 19:34

score 83 · Answer 12 · 2026-04-14 13:09:21

83

Views

How does the product $q_j X^j_m$ make sense in this context?

Published on 14 Apr 2026 - 13:09

score 252 · Answer 13 · 2026-04-15 22:00:49

252

Views

An equation of rational functions: $f(x)f(x+1)=\frac{g(x+1)}{g(x)}$

Published on 15 Apr 2026 - 22:00

score 104 · Answer 14 · 2026-04-14 12:19:52

104

Views

What are the integer coeffcients of a cubic polynomial having two particular properties?

Published on 14 Apr 2026 - 12:19

score 66 · Answer 15 · 2026-04-12 04:51:12

66

Views

Finding polynomials $p(-1)$

Published on 12 Apr 2026 - 4:51

List Question

What sufficient criteria are there for a polynomial to be separable?

Show that $x^{p^m} - x$ divides $x^{p^n} - x$ if and only if $m$ divides $n$.

Polynomials vector space and direct sums

Prove that if $f(x)$ divides $g(x)$ and $f(x)$ divides $h(x)$, then $f(x)$ divides $s(x)g(x) +t(x)h(x)$.

How do you prove that $\binom{n}{d} = \Theta(n^d)$?

characteristic polynomial with rows as coordinates

Why is 1, x and $x^2$ linearly independent?

Is it true that no polynomial (with the exception of constant polynomial) have an inverse in $\mathbb Z/p\mathbb Z$ (where p is prime)?

Proving the mean zero condition for polynomials over finite fields by linear algebra

Finding values for K such that the roots of the quadratic are strictly imaginary: $x^2+\left(K^2+3K-7\right)x+K$

Finding factors of polynomials without every power descending

How does the product $q_j X^j_m$ make sense in this context?

An equation of rational functions: $f(x)f(x+1)=\frac{g(x+1)}{g(x)}$

What are the integer coeffcients of a cubic polynomial having two particular properties?

Finding polynomials $p(-1)$

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