# New post in Gcd-and-lcm

July 26th, 2022

## What is the highest common factor of $n$ and $2n + 1$

December 6th, 2022

## Finding $d=\gcd(a,b)$; finding integers $m$ and $n$: $d=ma+nb$

August 15th, 2022

August 1st, 2022

## Greatest Common Divisor of prime numbers

September 18th, 2020

## greates number of baskets to put equal number of fruits

January 29th, 2021

June 16th, 2021

April 11th, 2020

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

February 18th, 2020

## Ladder method for lcm and gcd

January 5th, 2020

## Least number of cuts to share sausages equally

September 18th, 2020

## For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z$

September 1st, 2020

## For complex polynomials $\gcd(f,g)=1$ if and only if $f$ and $g$ have no common root

February 13th, 2020

August 1st, 2022

## $\gcd(a,b) = \gcd(a, a+2b)$ where $a$ is an odd integer

October 24th, 2020

March 15th, 2020

August 1st, 2022

August 1st, 2022

July 10th, 2021

## Prove that: $\gcd[a,b,c]=\frac{abc.\operatorname{lcm}(a,b,c)}{\operatorname{lcm}(a,b)\operatorname{lcm}(a,c)\operatorname{lcm}(b,c)}$

October 26th, 2020

## Let $H$ be a group. Let $a, b$ be fixed positive integers and $H=\{ax+by\mid x,y\in \Bbb Z\}.$ Show that $d\mathbb Z =H$ where $d=\gcd(a,b)$.

September 26th, 2020

April 19th, 2021

August 1st, 2022

## Let $q=gcd(x,y)$. Prove that if $x\nmid zq$ then $x \nmid yz$.

February 15th, 2020

August 1st, 2022

## Which of the following statements are true for all such $a$ and $b$? Prove the statement or give a counterexample.

September 24th, 2020

August 1st, 2022

## Proof that if $\gcd(m,n) = 1$, then $\gcd(m+n,mn ) = 1$.

December 3rd, 2020

August 1st, 2022

August 1st, 2022