Question

Proof checking Number theory: prove that $d\nmid a^{2^{n}}+1$.

score 95 · Answer 1 · 2016-04-10 13:47:00

95

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Proof checking Number theory: prove that $d\nmid a^{2^{n}}+1$.

Published on 10 Apr 2016 - 13:47

score 28 · Answer 2 · 2016-04-14 07:04:59

28

Views

$g$ is a primitive root of $p^s$, determine the form of all solutions to $x^{p-1} \equiv \pmod p^s$

Published on 14 Apr 2016 - 7:04

score 26 · Answer 3 · 2016-04-16 15:14:35

26

Views

Basis of the special form

Published on 16 Apr 2016 - 15:14

score 317 · Answer 4 · 2016-04-16 18:19:09

317

Views

Finding a primitive root modulo $p$

Published on 16 Apr 2016 - 18:19

score 399 · Answer 5 · 2016-04-16 20:05:27

399

Views

Show that 3 is a primitive root modulo 14. Then, write the other primitive roots modulo 14 in terms of powers of 3. How many are there?

Published on 16 Apr 2016 - 20:05

score 610 · Answer 6 · 2016-04-17 09:13:55

610

Views

If primitive root modulo $mn$, then primitive root modulo $m$ and $n$

Published on 17 Apr 2016 - 9:13

score 63 · Answer 7 · 2026-03-25 23:58:40

63

Views

let $q$ be a prime of the form $q=3r+1$ and assume that $p=4q+1$ is also a prime. Show that $3$ is a primitive root of $p$

Published on 25 Mar 2026 - 23:58

score 93 · Answer 8 · 2026-03-28 10:24:07

93

Views

Is $\mathbb{Q}(z,\dots,z^{n-1})$ the splitting field of some polynomial $\mathbb{Q}[x]$, where $z$ is a primitive root of unity?

Published on 28 Mar 2026 - 10:24

score 311 · Answer 9 · 2026-02-23 15:12:31

311

Views

can composite groups have primitive roots (be cyclic)?

Published on 23 Feb 2026 - 15:12

score 4k · Answer 10 · 2016-05-09 02:26:33

4k

Views

If $p$ is an odd prime and $k$ an integer with $0<k<p-1$ then $1^k + 2^k + \ldots + (p-1)^k$ is divisible by $p$

Published on 09 May 2016 - 2:26

score 147 · Answer 11 · 2016-05-13 01:22:06

147

Views

Congruence $16^{(x^ 2+x+1)} \equiv 4 \mod 11$

Published on 13 May 2016 - 1:22

score 149 · Answer 12 · 2016-05-13 10:10:33

149

Views

Showing that the polynomial $f = x^4+x^3+1 \in Z_2[x]$ is primitive?

Published on 13 May 2016 - 10:10

score 240 · Answer 13 · 2016-05-17 08:47:14

240

Views

primitive root modulo prime powers

Published on 17 May 2016 - 8:47

score 1.2k · Answer 14 · 2016-05-20 07:38:42

1.2k

Views

Find a primitive element in the splitting field of $x^4-8x^2+15$.

Published on 20 May 2016 - 7:38

score 404 · Answer 15 · 2016-06-01 08:25:34

404

Views

Solving $n^{th}$ power residue of a congruence

Published on 01 Jun 2016 - 8:25

List Question

Proof checking Number theory: prove that $d\nmid a^{2^{n}}+1$.

$g$ is a primitive root of $p^s$, determine the form of all solutions to $x^{p-1} \equiv \pmod p^s$

Basis of the special form

Finding a primitive root modulo $p$

Show that 3 is a primitive root modulo 14. Then, write the other primitive roots modulo 14 in terms of powers of 3. How many are there?

If primitive root modulo $mn$, then primitive root modulo $m$ and $n$

let $q$ be a prime of the form $q=3r+1$ and assume that $p=4q+1$ is also a prime. Show that $3$ is a primitive root of $p$

Is $\mathbb{Q}(z,\dots,z^{n-1})$ the splitting field of some polynomial $\mathbb{Q}[x]$, where $z$ is a primitive root of unity?

can composite groups have primitive roots (be cyclic)?

If $p$ is an odd prime and $k$ an integer with $0<k<p-1$ then $1^k + 2^k + \ldots + (p-1)^k$ is divisible by $p$

Congruence $16^{(x^ 2+x+1)} \equiv 4 \mod 11$

Showing that the polynomial $f = x^4+x^3+1 \in Z_2[x]$ is primitive?

primitive root modulo prime powers

Find a primitive element in the splitting field of $x^4-8x^2+15$.

Solving $n^{th}$ power residue of a congruence

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