List questions from gcd-and-lcm

Published on 16 Feb 2016 - 19:30

2.6k

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$ad-bc=1$, $w=au+bv$ and $z=cu+dv$. Prove $\gcd(u,v) = \gcd (w,z)$.

Published on 16 Feb 2016 - 23:27

1.5k

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Show that if $(x,y) =1$ then $(x-y, x+y)$ is either $1$ or $2$.

Published on 17 Feb 2016 - 10:35

784

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How to prove $\gcd(dm,dn)=d\cdot\gcd(m,n)$

Published on 17 Feb 2016 - 14:34

436

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Gcd(x^2+1,x+1) = {1 if x is even or 2 if x is odd?

Published on 18 Feb 2016 - 15:10

77

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proving euclid's algorithm stops after 2k iterations

Published on 28 Mar 2026 - 6:09

986

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Show that a positive integer $n \in \mathbb{N}$ is prime if and only if $\gcd(n,m)=1$ for all $0<n<m$.

Published on 20 Feb 2016 - 6:00

74

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finding a proof for a problem $(a+b,\frac{a^p+b^p}{a+b})=p$ or $1$

Published on 20 Feb 2016 - 7:08

676

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Solving for $x, y$ in $\gcd(a,b) = ax + by$

Published on 25 Mar 2026 - 22:10

544

Views

Euclidean Algorithm (gcd)

Published on 28 Mar 2026 - 6:05

536

Views

Greatest Common Divisor with Fibonacci Numbers

Published on 24 Feb 2016 - 5:53

1.6k

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Greatest common divisor of more than two numbers

Published on 25 Feb 2016 - 20:16

46

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GCF and differences of roots

Published on 25 Feb 2016 - 21:52

126

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a number n as pa+qb

Published on 26 Feb 2016 - 20:35

216

Views

If $a$ and $b$ are coprime, some integral combination is coprime to $c$

Published on 27 Feb 2016 - 0:40

List Question

Show that any two consecutive odd integers are relatively prime

$ad-bc=1$, $w=au+bv$ and $z=cu+dv$. Prove $\gcd(u,v) = \gcd (w,z)$.

Show that if $(x,y) =1$ then $(x-y, x+y)$ is either $1$ or $2$.

How to prove $\gcd(dm,dn)=d\cdot\gcd(m,n)$

Gcd(x^2+1,x+1) = {1 if x is even or 2 if x is odd?

proving euclid's algorithm stops after 2k iterations

Show that a positive integer $n \in \mathbb{N}$ is prime if and only if $\gcd(n,m)=1$ for all $0<n<m$.

finding a proof for a problem $(a+b,\frac{a^p+b^p}{a+b})=p$ or $1$

Solving for $x, y$ in $\gcd(a,b) = ax + by$

Euclidean Algorithm (gcd)

Greatest Common Divisor with Fibonacci Numbers

Greatest common divisor of more than two numbers

GCF and differences of roots

a number n as pa+qb

If $a$ and $b$ are coprime, some integral combination is coprime to $c$

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