Newbetuts

$\operatorname{lcm}(a,b) = c$ and $\gcd(a,b) = d$ => $\operatorname{lcm}(\frac{a}{d},\frac{b}{d}) = \frac{c}{d}$ in a Euclidean domain or PID

Prove by induction that $3^{2n+3}+40n-27$ is divisible by 64 for all n in natural numbers

$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime

If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$? [duplicate]

Proving that $\frac{n+1}{2n+3}$ and $\frac{3n-5}{4n-7}$ are irreducible for all $n$

Show that the numerator of $1+\frac12 +\frac13 +\cdots +\frac1{96}$ is divisible by $97$

Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer [closed]

Numbers $a$ such that if $a \mid b^2$ then $a \mid b$

Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)

Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.

Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime

My attempt to prove GCD exists

The number $n^4 + 4$ is never prime for $n>1$

How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?

New posts in divisibility

Prove that $2$, $3$, $1+ \sqrt{-5}$, and $1-\sqrt{-5}$ are irreducible in $\mathbb{Z}[\sqrt{-5}]$.

Showing that $m^2-n^2+1$ is a square

Showing $\gcd(n^3 + 1, n^2 + 2) = 1$, $3$, or $9$

Divisibility 1,2,3,4,5,6,7,8,9,&10

Mathematical Induction divisibility $8\mid 3^{2n}-1$

How to prove if $n$ is prime and $n | a^2$ then $n | a$?

$\operatorname{lcm}(a,b) = c$ and $\gcd(a,b) = d$ => $\operatorname{lcm}(\frac{a}{d},\frac{b}{d}) = \frac{c}{d}$ in a Euclidean domain or PID

Prove by induction that $3^{2n+3}+40n-27$ is divisible by 64 for all n in natural numbers

$\operatorname{gcd}(ab,a+b)=1$ if $a$ and $b$ are relatively prime

If $\gcd(a, b) = 1$ then prove that $\gcd(a+b, a^2-ab+b^2) = 1$ or $3$? [duplicate]

Proving that $\frac{n+1}{2n+3}$ and $\frac{3n-5}{4n-7}$ are irreducible for all $n$

Show that the numerator of $1+\frac12 +\frac13 +\cdots +\frac1{96}$ is divisible by $97$

Prove for positive integers a,b,c and d (where b does not equal d), if gcd(a,b) = gcd(c,d) = 1, then a/b + c/d is not an integer [closed]

Numbers $a$ such that if $a \mid b^2$ then $a \mid b$

Divisor of $m$ and $n$ divides $m - qn$ (in proof of Euclidean algorithm)

Let $a,k,m$ be integers. Prove that $\gcd(ka,km) = k\gcd(a,m)$.

Prove $4p-3$ is a square knowing that $n\mid p-1$ and $p\mid n^3-1$, $p$ prime

My attempt to prove GCD exists

The number $n^4 + 4$ is never prime for $n>1$

How to show that $7\mid a^2+b^2$ implies $7\mid a$ and $7\mid b$?