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Gcd-and-lcm
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Find all positive integers $a$ and $b$ satisfying $\gcd (a,b)=10$ and $\operatorname{lcm} (a,b)=100$ simultaneously.
July 26th, 2022
gcd-and-lcm
elementary-number-theory
number-theory
least-common-multiple
What is the highest common factor of $n$ and $2n + 1$
December 6th, 2022
gcd-and-lcm
elementary-number-theory
least-common-multiple
Finding $d=\gcd(a,b)$; finding integers $m$ and $n$: $d=ma+nb$
August 15th, 2022
euclidean-algorithm
gcd-and-lcm
Relation between GCD and LCM
August 1st, 2022
least-common-multiple
gcd-and-lcm
Greatest Common Divisor of prime numbers
September 18th, 2020
elementary-number-theory
gcd-and-lcm
greates number of baskets to put equal number of fruits
January 29th, 2021
least-common-multiple
gcd-and-lcm
Understanding recursive function for finding GCF of 2 numbers
June 16th, 2021
recursive-algorithms
gcd-and-lcm
recursion
Find the $\gcd(81,237)$ and express it as a linear combination of $81$ and $237.$
April 11th, 2020
gcd-and-lcm
divisibility
elementary-number-theory
Show that if $(x,y) =1$ then $(x-y, x+y)$ is either $1$ or $2$.
February 18th, 2020
elementary-number-theory
gcd-and-lcm
Ladder method for lcm and gcd
January 5th, 2020
gcd-and-lcm
least-common-multiple
Least number of cuts to share sausages equally
September 18th, 2020
gcd-and-lcm
least-common-multiple
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $
September 1st, 2020
gcd-and-lcm
divisibility
abstract-algebra
elementary-number-theory
For complex polynomials $\gcd(f,g)=1$ if and only if $f$ and $g$ have no common root
February 13th, 2020
gcd-and-lcm
polynomials
abstract-algebra
find and prove the necessary and sufficient condition in which (a,b)=[a,b]
August 1st, 2022
least-common-multiple
divisibility
gcd-and-lcm
$\gcd(a,b) = \gcd(a, a+2b)$ where $a$ is an odd integer
October 24th, 2020
gcd-and-lcm
discrete-mathematics
proof-verification
integers
elementary-number-theory
GCD of two big numbers
March 15th, 2020
gcd-and-lcm
Bezout's Identity and inverse modulo proof (GCD)
August 1st, 2022
modular-arithmetic
gcd-and-lcm
finding the greatest common divisor of two polynomial, I'm stuck
August 1st, 2022
polynomials
euclidean-algorithm
gcd-and-lcm
Prove that for any integer $k \ne 0$, $\gcd(k, k+1) = 1$
July 10th, 2021
number-theory
elementary-number-theory
gcd-and-lcm
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
number-theory
gcd-and-lcm
divisibility
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
abstract-algebra
group-theory
elementary-number-theory
cyclic-groups
gcd-and-lcm
Sum of two numbers $x, y = 1050$. What is the maximum value of the HCF between $x$ and $y$?
April 19th, 2021
elementary-number-theory
gcd-and-lcm
number-theory
solution-verification
Prove that if d is a common divisor of a and b, then $d=\gcd(a,b)$ if and only if $\gcd(a/d,b/d)=1$
August 1st, 2022
elementary-number-theory
gcd-and-lcm
Let $q=gcd(x,y)$. Prove that if $x\nmid zq$ then $x \nmid yz$.
February 15th, 2020
gcd-and-lcm
elementary-number-theory
greatest divisor of a number less than or equal to other number
August 1st, 2022
elementary-number-theory
gcd-and-lcm
Which of the following statements are true for all such $a$ and $b$? Prove the statement or give a counterexample.
September 24th, 2020
elementary-number-theory
gcd-and-lcm
Proof $ GCD(a,b) = GCD(a, b-a) = GCD (a, r_b) $
August 1st, 2022
proof-verification
gcd-and-lcm
elementary-number-theory
Proof that if $\gcd(m,n) = 1$, then $\gcd(m+n,mn ) = 1$.
December 3rd, 2020
gcd-and-lcm
elementary-number-theory
If gcd(a,c)=1 and b|c, then gcd(a,b)=1?
August 1st, 2022
discrete-mathematics
gcd-and-lcm
divisibility
proof-writing
Prove $\gcd(ka,kb)=k\cdot\gcd(a,b)$
August 1st, 2022
gcd-and-lcm
proof-verification
divisibility
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