Question

Let $p>2$ be a prime, $(a,p)=1,$ and suppose that $a^k$ is a primitive root mod $p$ for some $k>0$. Prove that $a$ itself is a primitive root.

score 391 · Answer 1 · 2026-04-20 14:34:45

Let $p>2$ be a prime, $(a,p)=1,$ and suppose that $a^k$ is a primitive root mod $p$ for some $k>0$. Prove that $a$ itself is a primitive root.

score 253 · Answer 2 · 2026-04-15 21:48:38

253

Views

$p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$

Published on 15 Apr 2026 - 21:48

score 51 · Answer 3 · 2026-04-20 14:37:02

51

Views

If $x^n \equiv a \space (31)$, how many values of n and a are there s.t there are only 10 solutions?

Published on 20 Apr 2026 - 14:37

score 39 · Answer 4 · 2026-04-12 06:12:08

39

Views

Clarification on Set notation

Published on 12 Apr 2026 - 6:12

score 372 · Answer 5 · 2026-04-10 01:52:38

372

Views

Higher derivatives $\wp^{(2n)}$ of the Weierstrass $\wp$-function

Published on 10 Apr 2026 - 1:52

score 385 · Answer 6 · 2026-04-10 22:05:19

385

Views

Bruhat and other decomposition of matrices

Published on 10 Apr 2026 - 22:05

score 63 · Answer 7 · 2026-04-11 11:16:33

63

Views

Fundamental assumption about number theory: divisibility

Published on 11 Apr 2026 - 11:16

score 240 · Answer 8 · 2026-04-13 07:08:30

240

Views

Invariant ring using GAP

Published on 13 Apr 2026 - 7:08

score 225 · Answer 9 · 2026-04-14 05:15:02

225

Views

the lowest positive integer number

Published on 14 Apr 2026 - 5:15

score 87 · Answer 10 · 2026-04-22 19:27:22

87

Views

Understanding Exact Formula for Sum of Divisors and how to program it

Published on 22 Apr 2026 - 19:27

score 98 · Answer 11 · 2026-04-10 19:45:34

98

Views

Probability not divisible by $k^2$

Published on 10 Apr 2026 - 19:45

score 75 · Answer 12 · 2026-03-24 23:45:52

75

Views

Finite formula for behaviour of infinite continued fractions

Published on 24 Mar 2026 - 23:45

score 85 · Answer 13 · 2026-04-15 20:01:37

85

Views

Can we find prime in the form of $2^nx+1$ for arbitrary $x>0$?

Published on 15 Apr 2026 - 20:01

score 195 · Answer 14 · 2026-04-11 23:45:23

195

Views

The origin of Lagrange numbers

Published on 11 Apr 2026 - 23:45

score 58 · Answer 15 · 2026-04-15 08:35:00

58

Views

Prove that $a^{20} = 1 \bmod 440$ if $\gcd(a,440)=1$.

Published on 15 Apr 2026 - 8:35

List Question

Let $p>2$ be a prime, $(a,p)=1,$ and suppose that $a^k$ is a primitive root mod $p$ for some $k>0$. Prove that $a$ itself is a primitive root.

$p\equiv 1,2,3\text{ mod }8 \Rightarrow p=a^2+2b^2\text{ for some $a,b\in\mathbb{Z}$.}$

If $x^n \equiv a \space (31)$, how many values of n and a are there s.t there are only 10 solutions?

Clarification on Set notation

Higher derivatives $\wp^{(2n)}$ of the Weierstrass $\wp$-function

Bruhat and other decomposition of matrices

Fundamental assumption about number theory: divisibility

Invariant ring using GAP

the lowest positive integer number

Understanding Exact Formula for Sum of Divisors and how to program it

Probability not divisible by $k^2$

Finite formula for behaviour of infinite continued fractions

Can we find prime in the form of $2^nx+1$ for arbitrary $x>0$?

The origin of Lagrange numbers

Prove that $a^{20} = 1 \bmod 440$ if $\gcd(a,440)=1$.

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