List questions from primitive-roots

Published on 27 Mar 2026 - 21:43

132

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coprime terms in the factorization of $x^p + y^p$

Published on 23 Feb 2026 - 12:05

50

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For every $k \in \Bbb Z$ there is $0 \le x \le p-1$ such as $x^3\equiv k \pmod {p}$

Published on 27 Mar 2026 - 22:00

70

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Finding a counter-example for Gaussian-periods for non-primes

Published on 27 Mar 2026 - 21:05

182

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Show that $101^2$ does not divide $2^{50}+1$ and that $2$ is a primitive root modulo $101^{101}$

Published on 28 Jun 2020 - 19:47

150

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Is there a deeper reason for the classification of moduli in which a primitive root exists?

Published on 30 Jun 2020 - 0:50

43

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Quadratic number fields that contain primitive root of unity

Published on 25 Mar 2026 - 11:34

61

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Prove that $7$ is a primitive root modulo $p=2^s+1$.

Published on 08 Jul 2020 - 19:17

81

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Proving two distinct primitive roots do not generate $\mathbb{Z}^{\times}_n$ in the same order

Published on 17 Jul 2020 - 4:49

380

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Show that $2$ is a primitive root $\mod{3^k}$ for all positive $k$

Published on 27 Jul 2020 - 8:29

166

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Prove that Carmichael number has no primitive roots

Published on 06 Jul 2016 - 5:53

87

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Solve $19^n$ = $801777482$ $\pmod {4535332489}$ given $4535332489$ is prime.

Published on 16 Jul 2016 - 23:20

402

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Are there infinitely many primes $n$ such that $\mathbb{Z}_n^*$ is generated by $\{ -1,2 \}$?

Published on 18 Jul 2016 - 0:11

251

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A field of Radical Sums

Published on 25 Mar 2026 - 8:09

138

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Help with primitive root modulo $p^r$

Published on 02 Aug 2016 - 17:50

List Question

Primitive root modulo $2p$

coprime terms in the factorization of $x^p + y^p$

For every $k \in \Bbb Z$ there is $0 \le x \le p-1$ such as $x^3\equiv k \pmod {p}$

Finding a counter-example for Gaussian-periods for non-primes

Show that $101^2$ does not divide $2^{50}+1$ and that $2$ is a primitive root modulo $101^{101}$

Is there a deeper reason for the classification of moduli in which a primitive root exists?

Quadratic number fields that contain primitive root of unity

Prove that $7$ is a primitive root modulo $p=2^s+1$.

Proving two distinct primitive roots do not generate $\mathbb{Z}^{\times}_n$ in the same order

Show that $2$ is a primitive root $\mod{3^k}$ for all positive $k$

Prove that Carmichael number has no primitive roots

Solve $19^n$ = $801777482$ $\pmod {4535332489}$ given $4535332489$ is prime.

Are there infinitely many primes $n$ such that $\mathbb{Z}_n^*$ is generated by $\{ -1,2 \}$?

A field of Radical Sums

Help with primitive root modulo $p^r$

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