Question

Number Theory: Modular Arithmetic Orders and Primitive Roots

score 620 · Answer 1 · 2015-11-09 06:43:31

620

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Number Theory: Modular Arithmetic Orders and Primitive Roots

Published on 09 Nov 2015 - 6:43

score 262 · Answer 2 · 2026-03-15 07:50:23

262

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Number Theory: Prove $x^k\equiv a\pmod{p}$ is solvable for $r^d,r^{2d},\dots,r^{[(p-1)/d]d}$.

Published on 15 Mar 2026 - 7:50

score 1k · Answer 3 · 2015-11-19 22:16:49

1k

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Number Theory: Prove that any primitive root $r$ of $p^n$ is also a primitive root of $p$

Published on 19 Nov 2015 - 22:16

score 244 · Answer 4 · 2026-03-27 19:10:04

244

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Primitive root pairs

Published on 27 Mar 2026 - 19:10

score 169 · Answer 5 · 2026-03-28 21:04:12

169

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Solve $ x^2 = 2$ over $ F_5 $.

Published on 28 Mar 2026 - 21:04

score 53 · Answer 6 · 2015-11-28 21:05:38

53

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Let $\xi_{19} \in G_{19}$ be a primitive root of unity. Find $\Re\sum_{k=1}^9\xi_{19}^{k^2}$.

Published on 28 Nov 2015 - 21:05

score 70 · Answer 7 · 2015-11-30 16:36:05

70

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$n\in\mathbb{N}$ such that for every divisor $d$ of $\phi(n)$ there exist a element with order $d$ modulo $n$

Published on 30 Nov 2015 - 16:36

score 546 · Answer 8 · 2015-12-08 06:15:51

546

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Number Theory: Find a primitive root of $13^{901}$ and find a complete set of primitive roots of $13$

Published on 08 Dec 2015 - 6:15

score 1.4k · Answer 9 · 2015-12-08 07:48:10

1.4k

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Find all incongruent solutions of $x^8\equiv3\pmod{13}$.

Published on 08 Dec 2015 - 7:48

score 111 · Answer 10 · 2026-03-26 06:31:08

111

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a ≡ b mod p implies that $(\frac {a}{p}) =(\frac {b}{p})$ The Legendre Symbol

Published on 26 Mar 2026 - 6:31

score 1.5k · Answer 11 · 2015-12-14 00:14:44

1.5k

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nth root of unity in a cyclic group $\mathbb{Z}_p^*$

Published on 14 Dec 2015 - 0:14

score 56 · Answer 12 · 2015-12-15 22:50:25

56

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Suppose $(a+i)^{a+i}\equiv a^a \mod p$ for all $a=1,2,..$ Then $i$ is divisible by $p(p-1)$

Published on 15 Dec 2015 - 22:50

score 440 · Answer 13 · 2015-12-17 20:33:11

440

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$g$ is a primitive root mod $p$ and $h$ is a primitive root mod $q$. Using CRT find $k$ whose order is exactly lcm$(p-1,q-1)$

Published on 17 Dec 2015 - 20:33

score 1.1k · Answer 14 · 2015-12-31 15:13:19

1.1k

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What is the sum of ALL of the nth powers of the qth roots of unity?

Published on 31 Dec 2015 - 15:13

score 119 · Answer 15 · 2016-01-01 09:03:16

119

Views

Lower bound for the values of cyclotomic polynomials evualuated at integers

Published on 01 Jan 2016 - 9:03

List Question

Number Theory: Modular Arithmetic Orders and Primitive Roots

Number Theory: Prove $x^k\equiv a\pmod{p}$ is solvable for $r^d,r^{2d},\dots,r^{[(p-1)/d]d}$.

Number Theory: Prove that any primitive root $r$ of $p^n$ is also a primitive root of $p$

Primitive root pairs

Solve $ x^2 = 2$ over $ F_5 $.

Let $\xi_{19} \in G_{19}$ be a primitive root of unity. Find $\Re\sum_{k=1}^9\xi_{19}^{k^2}$.

$n\in\mathbb{N}$ such that for every divisor $d$ of $\phi(n)$ there exist a element with order $d$ modulo $n$

Number Theory: Find a primitive root of $13^{901}$ and find a complete set of primitive roots of $13$

Find all incongruent solutions of $x^8\equiv3\pmod{13}$.

a ≡ b mod p implies that $(\frac {a}{p}) =(\frac {b}{p})$ The Legendre Symbol

nth root of unity in a cyclic group $\mathbb{Z}_p^*$

Suppose $(a+i)^{a+i}\equiv a^a \mod p$ for all $a=1,2,..$ Then $i$ is divisible by $p(p-1)$

$g$ is a primitive root mod $p$ and $h$ is a primitive root mod $q$. Using CRT find $k$ whose order is exactly lcm$(p-1,q-1)$

What is the sum of ALL of the nth powers of the qth roots of unity?

Lower bound for the values of cyclotomic polynomials evualuated at integers

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