Question

Prove subgroups of cyclic groups are cyclic without division algorithm, rings, homomorphisms or $\gcd$ of infinite numbers?

score 289 · Answer 1 · 2018-10-10 11:55:28

289

Views

Prove subgroups of cyclic groups are cyclic without division algorithm, rings, homomorphisms or $\gcd$ of infinite numbers?

Published on 10 Oct 2018 - 11:55

score 544 · Answer 2 · 2026-03-25 06:06:50

544

Views

For polynomials $f, g$ and $\gcd(f(X),g(X))=d(X)$ then $\gcd(f(X+a),g(X+a))=d(X+a)$

Published on 25 Mar 2026 - 6:06

score 44 · Answer 3 · 2026-03-25 06:04:05

44

Views

$\gcd(x,y)=1$ then $\gcd(c \cdot x, c \cdot y)=c$ for polynomials

Published on 25 Mar 2026 - 6:04

score 510 · Answer 4 · 2018-10-13 12:25:13

510

Views

Prove that gcd$(n^2+1, (n+1)^2+1)$ is either 1 or 5

Published on 13 Oct 2018 - 12:25

score 2k · Answer 5 · 2018-10-15 18:26:01

2k

Views

How many number of integer coordinates exists between a line segment, including the end points?

Published on 15 Oct 2018 - 18:26

score 177 · Answer 6 · 2018-10-15 21:54:46

177

Views

Euclidean GCD calculation and mod

Published on 15 Oct 2018 - 21:54

score 101 · Answer 7 · 2018-10-17 12:22:10

101

Views

Gcd of two elements

Published on 17 Oct 2018 - 12:22

score 1.3k · Answer 8 · 2026-03-25 13:58:09

1.3k

Views

Let $\theta$ be a root of $p(x)=x^3+9x+6$, find the inverse of $1+\theta$ in $\mathbb{Q(\theta)}$

Published on 25 Mar 2026 - 13:58

score 95 · Answer 9 · 2026-03-25 13:54:42

95

Views

Extended GCD of two zero polynomials over finite field

Published on 25 Mar 2026 - 13:54

score 574 · Answer 10 · 2018-10-18 21:05:53

574

Views

Find all possible values of $(7a+12,3a+5)$.

Published on 18 Oct 2018 - 21:05

score 693 · Answer 11 · 2018-10-18 23:55:29

693

Views

With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$

Published on 18 Oct 2018 - 23:55

score 143 · Answer 12 · 2018-10-19 10:47:32

143

Views

Let $a\mid bc $ then prove or disprove $a\mid (a,b)c$

Published on 19 Oct 2018 - 10:47

score 187 · Answer 13 · 2018-10-21 13:57:48

187

Views

Greatest Common Divisor question (involving Bezout's theorem)

Published on 21 Oct 2018 - 13:57

score 90 · Answer 14 · 2026-02-23 01:05:34

90

Views

Is there at least one pair from $a, b, c$ that is coprime?

Published on 23 Feb 2026 - 1:05

score 79 · Answer 15 · 2018-10-22 01:02:46

79

Views

Prove that the $GCD(2^{k}, n) = 1$ given that $GCD(2, n) = 1 $ and n is odd

Published on 22 Oct 2018 - 1:02

List Question

Prove subgroups of cyclic groups are cyclic without division algorithm, rings, homomorphisms or $\gcd$ of infinite numbers?

For polynomials $f, g$ and $\gcd(f(X),g(X))=d(X)$ then $\gcd(f(X+a),g(X+a))=d(X+a)$

$\gcd(x,y)=1$ then $\gcd(c \cdot x, c \cdot y)=c$ for polynomials

Prove that gcd$(n^2+1, (n+1)^2+1)$ is either 1 or 5

How many number of integer coordinates exists between a line segment, including the end points?

Euclidean GCD calculation and mod

Gcd of two elements

Let $\theta$ be a root of $p(x)=x^3+9x+6$, find the inverse of $1+\theta$ in $\mathbb{Q(\theta)}$

Extended GCD of two zero polynomials over finite field

Find all possible values of $(7a+12,3a+5)$.

With $a,\ b,\ m,\ n\in \mathbb{Z}$. Show that if ${\rm gcd}(m,n)=1$, then ${\rm gcd}(ma+nb,mn)={\rm gcd}(a,n){\rm gcd}(b,m)$

Let $a\mid bc $ then prove or disprove $a\mid (a,b)c$

Greatest Common Divisor question (involving Bezout's theorem)

Is there at least one pair from $a, b, c$ that is coprime?

Prove that the $GCD(2^{k}, n) = 1$ given that $GCD(2, n) = 1 $ and n is odd

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