Question

Let $G$ be a finite group and let g ∈ G be an element with order d. Let i ∈ ℤ. Show that the order of $g^{i} $ is $d/\gcd(i,d)$\

score 283 · Answer 1 · 2020-02-18 12:17:51

283

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Let $G$ be a finite group and let g ∈ G be an element with order d. Let i ∈ ℤ. Show that the order of $g^{i} $ is $d/\gcd(i,d)$\

Published on 18 Feb 2020 - 12:17

score 969 · Answer 2 · 2026-03-26 09:47:39

969

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Can someone explain to me why the greatest common factor of (a,b) is equal to gcf(a mod b, a)

Published on 26 Mar 2026 - 9:47

score 297 · Answer 3 · 2020-02-20 17:24:00

Prove that $\operatorname{lcm}(a,b,c)=\frac{abc \operatorname{gcd}(a,b,c)} {\operatorname{gcd}(a,b)\operatorname{gcd}(b,c)\operatorname{gcd}(c,a)}$

score 132 · Answer 4 · 2020-02-22 04:50:58

132

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Is $\sum_{n=1}^{\infty} \frac{1}{\operatorname{lcm}[1,~2,~\ldots,~n]}$ irrational?

Published on 22 Feb 2020 - 4:50

score 541 · Answer 5 · 2020-02-22 15:12:48

541

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Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?

Published on 22 Feb 2020 - 15:12

score 53 · Answer 6 · 2020-02-22 16:42:18

53

Views

Question regarding $\gcd(a,b)=\gcd(b,r)$

Published on 22 Feb 2020 - 16:42

score 1.3k · Answer 7 · 2020-02-25 20:41:43

1.3k

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GCD of polynomials over GF(2)

Published on 25 Feb 2020 - 20:41

score 203 · Answer 8 · 2020-02-26 01:23:27

203

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Proving GCD's are equal

Published on 26 Feb 2020 - 1:23

score 127 · Answer 9 · 2020-02-26 03:55:35

127

Views

Show that if $\gcd(a,b) = 1$ and $a|n$, $b|n$ then $ab|n$

Published on 26 Feb 2020 - 3:55

score 231 · Answer 10 · 2020-02-27 21:39:43

231

Views

Understanding the proof of Russian Olympic question

Published on 27 Feb 2020 - 21:39

score 71 · Answer 11 · 2020-02-28 03:26:23

71

Views

Sequence is defined by $a_0 = 3$, $a_1 = 7$ and $a_n = 2^na_{n-1}+(-1)^na_{n-2}$. Prove that gcd($a_n,a_{n-1}$) = 1 for all natural numbers n.

Published on 28 Feb 2020 - 3:26

score 1.2k · Answer 12 · 2020-03-01 06:53:05

1.2k

Views

How to find one unknown number while LCM and GCD is given?

Published on 01 Mar 2020 - 6:53

score 3.5k · Answer 13 · 2026-03-27 21:35:43

3.5k

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Signal - How to determine the fundamental frequency of a signal

Published on 27 Mar 2026 - 21:35

score 84 · Answer 14 · 2020-03-07 23:22:26

84

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$(a, b)$ pairs with $\gcd(a, b) = 1$

Published on 07 Mar 2020 - 23:22

score 83 · Answer 15 · 2020-03-08 12:08:35

83

Views

How do I solve $\gcd(k+8,18)=1$ when $k$ is an integer

Published on 08 Mar 2020 - 12:08

List Question

Let $G$ be a finite group and let g ∈ G be an element with order d. Let i ∈ ℤ. Show that the order of $g^{i} $ is $d/\gcd(i,d)$\

Can someone explain to me why the greatest common factor of (a,b) is equal to gcf(a mod b, a)

Prove that $\operatorname{lcm}(a,b,c)=\frac{abc \operatorname{gcd}(a,b,c)} {\operatorname{gcd}(a,b)\operatorname{gcd}(b,c)\operatorname{gcd}(c,a)}$

Is $\sum_{n=1}^{\infty} \frac{1}{\operatorname{lcm}[1,~2,~\ldots,~n]}$ irrational?

Show that if $\gcd(a,3)=1$ then $a^7 \equiv a\pmod{63}$. Why is this assumption necessary?

Question regarding $\gcd(a,b)=\gcd(b,r)$

GCD of polynomials over GF(2)

Proving GCD's are equal

Show that if $\gcd(a,b) = 1$ and $a|n$, $b|n$ then $ab|n$

Understanding the proof of Russian Olympic question

Sequence is defined by $a_0 = 3$, $a_1 = 7$ and $a_n = 2^na_{n-1}+(-1)^na_{n-2}$. Prove that gcd($a_n,a_{n-1}$) = 1 for all natural numbers n.

How to find one unknown number while LCM and GCD is given?

Signal - How to determine the fundamental frequency of a signal

$(a, b)$ pairs with $\gcd(a, b) = 1$

How do I solve $\gcd(k+8,18)=1$ when $k$ is an integer

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