Newbetuts

There is a number divisible by all integers from 1 to 200, except for two consecutive numbers. What are the two?

$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$

$(a^{2^n}+1,a^{2^m}+1)=1 or 2$ [duplicate]

Prove Order of $x^k = n/{\gcd(k,n)}$ by taking cases

If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$ [duplicate]

True or False: $\operatorname{gcd}(a,b) = \operatorname{gcd}(5a+b, 3a+2b)$

If $m=\operatorname{lcm}(a,b)$ then $\gcd(\frac{m}{a},\frac{m}{b})=1$

Prove GCD of polynomials is same when coefficients are in a different field

Show that $\rm lcm(a,b)=ab \iff gcd(a,b)=1$

If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$. [duplicate]

If $a^3+a^2+a=9b^3+b^2+b$ and $a,b$ are integers then show $a-b$ is a perfect cube.

How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?

Proof that the ratio between the logs of the product and LCM of the Fibonacci numbers converges to $\frac{\pi^2}{6}$

Prove if a (mod n) has a multiplicative inverse, then it's unique

Simple example of non-arithmetic ring (non-distributive ideal lattice)

LCM is associative: $\ \text{lcm}(\text{lcm}(a,b),c)=\text{lcm}(a,\text{lcm}(b,c))$

If a and b are relatively prime and ab is a square, then a and b are squares.

New posts in gcd-and-lcm

Suppose $(a,b)=1$, then $(2a+b,a+2b)=1\text{ or }3$.

One of any consecutive integers is coprime to the rest

If $\gcd(a,b)=d$, then $\gcd(ac,bc)=cd$?

There is a number divisible by all integers from 1 to 200, except for two consecutive numbers. What are the two?

$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$

$(a^{2^n}+1,a^{2^m}+1)=1 or 2$ [duplicate]

Prove Order of $x^k = n/{\gcd(k,n)}$ by taking cases

If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$ [duplicate]

True or False: $\operatorname{gcd}(a,b) = \operatorname{gcd}(5a+b, 3a+2b)$

If $m=\operatorname{lcm}(a,b)$ then $\gcd(\frac{m}{a},\frac{m}{b})=1$

Prove GCD of polynomials is same when coefficients are in a different field

Show that $\rm lcm(a,b)=ab \iff gcd(a,b)=1$

If $\gcd(a,n) = 1$ and $\gcd(b,n) = 1$, then $\gcd(ab,n) = 1$. [duplicate]

If $a^3+a^2+a=9b^3+b^2+b$ and $a,b$ are integers then show $a-b$ is a perfect cube.

How can I prove that $\gcd(a,b)=1\implies \gcd(a^2,b^2)=1$ without using prime decomposition?

Proof that the ratio between the logs of the product and LCM of the Fibonacci numbers converges to $\frac{\pi^2}{6}$

Prove if a (mod n) has a multiplicative inverse, then it's unique

Simple example of non-arithmetic ring (non-distributive ideal lattice)

LCM is associative: $\ \text{lcm}(\text{lcm}(a,b),c)=\text{lcm}(a,\text{lcm}(b,c))$

If a and b are relatively prime and ab is a square, then a and b are squares.