New posts in gcd-and-lcm

Prove that $gcd((a^{n}-b^{n})/(a-b), a-b) = gcd(n(a,b)^{n-1}, a-b)$ for a,b $\in$ $\mathbb{Z}^+$ [duplicate]

number-theory elementary-number-theory divisibility gcd-and-lcm

Multiplicative inverse of $n+1$ modulo $n^2$ [duplicate]

elementary-number-theory modular-arithmetic gcd-and-lcm

Prove that if $a$ and $b$ are odd, coprime numbers, then $\gcd(2^a +1, 2^b +1) = 3$

elementary-number-theory gcd-and-lcm

Prove that if $\gcd(a,b)=1$, then $\gcd(a\cdot b,c) = \gcd(a,c)\cdot \gcd(b,c)$. [duplicate]

elementary-number-theory gcd-and-lcm

When does $\gcd(m,\sigma(m^2))$ equal $\gcd(m^2,\sigma(m^2))$? What are the exceptions?

number-theory elementary-number-theory gcd-and-lcm divisor-sum arithmetic-functions

Express $ \operatorname{gcd}\left(5^{m}+7^{m}, 5^{n}+7^{n}\right) $ in terms of $m$ and $n$

elementary-number-theory contest-math gcd-and-lcm

If $ar + bs =1$, then $\gcd(a,s) = \gcd(r,b) = \gcd(r,s) = 1$ [duplicate]

elementary-number-theory proof-writing divisibility gcd-and-lcm

Show that $\gcd(3k+2,5k+3)=1$

elementary-number-theory gcd-and-lcm

Prove that $\gcd{\left(\binom M1,\binom M2,\binom M3,\ldots,\binom Mn\right)}=1$ where $M=\mathrm{lcm}(1,2,3,\ldots,n)$

number-theory elementary-number-theory binomial-coefficients gcd-and-lcm

Prove that if $\gcd(a,b)=1$ then $\gcd(ab,c) = \gcd(a,c) \gcd(b,c)$

elementary-number-theory divisibility gcd-and-lcm

If a power of 2 divides a number, under what conditions does it divide a binomial coefficient involving the number that it divides?

combinatorics number-theory binomial-coefficients divisibility gcd-and-lcm

Let $m \in \mathbb{Z^+} , n \in \mathbb{Z^+}$ and let $d=\gcd(m,n)$. Prove that $m\mathbb{Z}+n\mathbb{Z}=d\mathbb{Z}$

abstract-algebra elementary-number-theory gcd-and-lcm

True or false : $\gcd(a_m, a_n) = a_{\gcd(m, n)}$?

number-theory polynomials gcd-and-lcm

Calculating the gcd of complex numbers

number-theory elementary-number-theory complex-numbers gcd-and-lcm

Euclidean Algorithm for GCD of polynomials

elementary-number-theory polynomials gcd-and-lcm

Why the $GCD$ of any two consecutive Fibonacci numbers is $1$?

elementary-number-theory binomial-coefficients divisibility fibonacci-numbers gcd-and-lcm

Using GCD with remainder to list all the integer elements in the set

elementary-number-theory gcd-and-lcm euclidean-algorithm

How to prove that $\gcd(m^2,m+n) = \gcd(n^2,m+n)$ [duplicate]

elementary-number-theory divisibility gcd-and-lcm

Denominator in rational gcd of integer polynomials

abstract-algebra elementary-number-theory polynomials gcd-and-lcm

Does $\gcd(a,bc)$ divides $\gcd(a, b)\gcd(a, c)$?

abstract-algebra elementary-number-theory divisibility gcd-and-lcm