Newbetuts

Find, with proof, all the integers $a$ that satisfy the equation $\gcd\left(a,\:10\right)\:=\:a.$ [duplicate]

Division in $1$ variable

Find all $x,y,z\in\mathbb N$, $x,y,z>1$ such that satisfy $x\mid yz+1$, $y\mid xz+1$, and $z\mid xy+1$

Describing all $f \in \mathbb{F}_2[x]$ divisible by $x^2 +1$

if $k > 1$ and $m\ge 1$ are such that $a^k = (2^m-1)(2^m+1)$, then does $a | 2^m-1$ or $a| 2^m+1$

For all integers a, b, c, if a | b and b | c then a | c. [duplicate]

What is the probability of a random natural number being a power of $10$

Proof of divisibility with combinatorics

The number of positive integers less than 1000 with an odd number of divisors

Is a function of $\mathbb N$ known producing only prime numbers?

Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime

Division rules for other number systems? [duplicate]

Linear congruence fill in the missing step?

The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.

Does it follow that $(n!)^n$ divide $(n^2)!$

If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$

New posts in divisibility

What are the possible prime factors of $3^n+2$ , where $n$ is a positive integer?

Are there infinitely many pairs of primes where each divides one more than the square of the other?

$ 7\mid x \text{ and } 7\mid y \Longleftrightarrow 7\mid x^2+y^2 $

Can the identity $ab=\gcd(a,b)\text{lcm}(a,b)$ be recovered from this category?

Find, with proof, all the integers $a$ that satisfy the equation $\gcd\left(a,\:10\right)\:=\:a.$ [duplicate]

Division in $1$ variable

Find all $x,y,z\in\mathbb N$, $x,y,z>1$ such that satisfy $x\mid yz+1$, $y\mid xz+1$, and $z\mid xy+1$

Describing all $f \in \mathbb{F}_2[x]$ divisible by $x^2 +1$

if $k > 1$ and $m\ge 1$ are such that $a^k = (2^m-1)(2^m+1)$, then does $a | 2^m-1$ or $a| 2^m+1$

For all integers a, b, c, if a | b and b | c then a | c. [duplicate]

What is the probability of a random natural number being a power of $10$

Proof of divisibility with combinatorics

The number of positive integers less than 1000 with an odd number of divisors

Is a function of $\mathbb N$ known producing only prime numbers?

Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime

Division rules for other number systems? [duplicate]

Linear congruence fill in the missing step?

The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.

Does it follow that $(n!)^n$ divide $(n^2)!$

If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$