Question

Prime factorisation: Show that if $(a | (b \cdot c) \text{ and } \text{gcd}(a,c) = 1) \Rightarrow a|b$

score 94 · Answer 1 · 2016-10-31 16:25:47

94

Views

Prime factorisation: Show that if $(a | (b \cdot c) \text{ and } \text{gcd}(a,c) = 1) \Rightarrow a|b$

Published on 31 Oct 2016 - 16:25

score 34 · Answer 2 · 2016-11-01 10:46:55

34

Views

Given $(b, m)$, how can we come up with $(b, m) = (b + mx, m)$?

Published on 01 Nov 2016 - 10:46

score 108 · Answer 3 · 2016-11-01 19:02:27

108

Views

Given integers $a$ and $b$ prove that if there exist integers $x$ and $y$ for which $ax+by=(a,b)$ then $(x,y)=1.$

Published on 01 Nov 2016 - 19:02

score 120 · Answer 4 · 2026-03-25 14:26:58

120

Views

How to prove if $px+qy=r$ has an integer solution, then it has infinite integer solutions $(x,y)$ with $x$ being even or $y$ being even

Published on 25 Mar 2026 - 14:26

score 51 · Answer 5 · 2016-11-02 02:45:46

51

Views

Computing $\gcd of\left(\left(5\displaystyle\prod_{i=1}^{7}63^i\right)^{10},~135^{135}\right)$

Published on 02 Nov 2016 - 2:45

score 870 · Answer 6 · 2026-03-27 10:10:58

870

Views

Prove that if ax+by=c has an integer solution, then it has infinitely many integer solutions (x, y) where x is even or y is even.

Published on 27 Mar 2026 - 10:10

score 497 · Answer 7 · 2016-11-02 08:28:46

497

Views

Assuming that $\gcd(a,b)=1$, show that $\gcd(a+b,a^2+b^2)=1$ or $2$.

Published on 02 Nov 2016 - 8:28

score 865 · Answer 8 · 2016-11-02 10:38:10

865

Views

Group $G$ of order $n$. $b^m$ with $\gcd(m,n)=1$

Published on 02 Nov 2016 - 10:38

score 129 · Answer 9 · 2016-11-03 20:38:25

129

Views

Does this "formula" calculate the largest odd divisor of $n^2+1$ ?

Published on 03 Nov 2016 - 20:38

score 197 · Answer 10 · 2016-11-03 22:41:22

197

Views

How do I prove that 15462227 and 15462229 relatively prime?

Published on 03 Nov 2016 - 22:41

score 108 · Answer 11 · 2016-11-03 23:02:18

108

Views

Find gcd(15570555, 10872579)

Published on 03 Nov 2016 - 23:02

score 342 · Answer 12 · 2016-11-04 04:08:04

342

Views

Evaluation of the $\gcd (x^2-x+1, x^3+2x+2)$ in $\mathbb{Z_3}[x]$

Published on 04 Nov 2016 - 4:08

score 3.9k · Answer 13 · 2016-11-04 07:19:05

3.9k

Views

Let $m$ and $n$ be positive integers such that $\gcd(m,n)=1.$Compute $\gcd(5^m+7^m,5^n+7^n)$.

Published on 04 Nov 2016 - 7:19

score 94 · Answer 14 · 2016-11-05 12:27:31

94

Views

Another proof that if $(a,b)=1$, then$(a+b,a-b) = 1$ or $2$

Published on 05 Nov 2016 - 12:27

score 192 · Answer 15 · 2016-11-05 21:11:09

192

Views

How do i show that :$\sum_{i=1}^{n} \frac{1}{a_i}<2 $ using both $\ Lcm $, and $\gcd$?

Published on 05 Nov 2016 - 21:11

List Question

Prime factorisation: Show that if $(a | (b \cdot c) \text{ and } \text{gcd}(a,c) = 1) \Rightarrow a|b$

Given $(b, m)$, how can we come up with $(b, m) = (b + mx, m)$?

Given integers $a$ and $b$ prove that if there exist integers $x$ and $y$ for which $ax+by=(a,b)$ then $(x,y)=1.$

How to prove if $px+qy=r$ has an integer solution, then it has infinite integer solutions $(x,y)$ with $x$ being even or $y$ being even

Computing $\gcd of\left(\left(5\displaystyle\prod_{i=1}^{7}63^i\right)^{10},~135^{135}\right)$

Prove that if ax+by=c has an integer solution, then it has infinitely many integer solutions (x, y) where x is even or y is even.

Assuming that $\gcd(a,b)=1$, show that $\gcd(a+b,a^2+b^2)=1$ or $2$.

Group $G$ of order $n$. $b^m$ with $\gcd(m,n)=1$

Does this "formula" calculate the largest odd divisor of $n^2+1$ ?

How do I prove that 15462227 and 15462229 relatively prime?

Find gcd(15570555, 10872579)

Evaluation of the $\gcd (x^2-x+1, x^3+2x+2)$ in $\mathbb{Z_3}[x]$

Let $m$ and $n$ be positive integers such that $\gcd(m,n)=1.$Compute $\gcd(5^m+7^m,5^n+7^n)$.

Another proof that if $(a,b)=1$, then$(a+b,a-b) = 1$ or $2$

How do i show that :$\sum_{i=1}^{n} \frac{1}{a_i}<2 $ using both $\ Lcm $, and $\gcd$?

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