If $f$ is an integer coefficient polynomial and $n$ is square free, does $f(\frac{1+\sqrt n}{2})=f(\frac{1-\sqrt n}{2})$ imply that $f$ is an integer?

score 834 · Answer 7 · 2026-04-15 00:05:18

834

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Dimension of incidence variety

Published on 15 Apr 2026 - 0:05

score 371 · Answer 8 · 2026-04-16 06:07:38

Find polynomial over Z2, that has the least degree, for which the field P=GF(64) is the minimum decomposition field. How much such polynomial are?

score 1.9k · Answer 9 · 2026-05-10 17:00:21

1.9k

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Group of order $|G|=6545$ has either a normal Sylow 5-subgroup or a normal Sylow 17-subgroup.

Published on 10 May 2026 - 17:00

score 284 · Answer 10 · 2026-04-14 17:39:09

284

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Let $K$ be a field, Splitting field $L$ over $K$ of polynomial $f(x)=x^n-\theta$

Published on 14 Apr 2026 - 17:39

score 64 · Answer 11 · 2026-04-13 06:45:55

64

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Given the splitting field $L$ and a field $K$, Find $Aut(L/K)$

Published on 13 Apr 2026 - 6:45

score 27 · Answer 12 · 2026-04-14 19:27:42

27

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Completing a polynomial in $\mathbb Z[\frac{1+\sqrt n}{2}][x]$ to a polynomial in $\mathbb Z[x]$ ($n=4k+1$).

Published on 14 Apr 2026 - 19:27

score 174 · Answer 13 · 2026-04-11 13:11:38

174

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Proving a ring homomorphism for the ring of integers over its ideal

Published on 11 Apr 2026 - 13:11

score 200 · Answer 14 · 2026-05-15 01:55:36

200

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Subgame Nash Equlibrium

Published on 15 May 2026 - 1:55

score 218 · Answer 15 · 2026-04-14 15:20:13

218

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integral k-algebra and geometrically integral k-algebra

Published on 14 Apr 2026 - 15:20

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If $f$ is an integer coefficient polynomial and $n$ is square free, does $f(\frac{1+\sqrt n}{2})=f(\frac{1-\sqrt n}{2})$ imply that $f$ is an integer?

Dimension of incidence variety

Find polynomial over Z2, that has the least degree, for which the field P=GF(64) is the minimum decomposition field. How much such polynomial are?

Group of order $|G|=6545$ has either a normal Sylow 5-subgroup or a normal Sylow 17-subgroup.

Let $K$ be a field, Splitting field $L$ over $K$ of polynomial $f(x)=x^n-\theta$

Given the splitting field $L$ and a field $K$, Find $Aut(L/K)$

Completing a polynomial in $\mathbb Z[\frac{1+\sqrt n}{2}][x]$ to a polynomial in $\mathbb Z[x]$ ($n=4k+1$).

Proving a ring homomorphism for the ring of integers over its ideal

Subgame Nash Equlibrium

integral k-algebra and geometrically integral k-algebra

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