New posts in divisibility

Every prime number divide some sum of the first $k$ primes.

prime-numbers divisibility conjectures

Do there exist infinitely many pairs of primes $(p,q)$ such that $pq$ divides $2^{p-1}+2^{q-1}-2$?

elementary-number-theory prime-numbers divisibility

Proving divisibility of $a^3 - a$ by $6$ [duplicate]

UFD, prime and Irreducible

abstract-algebra ring-theory divisibility

Show that if $ar + bs = 1$ for some $r$ and $s$ then $a$ and $b$ are relatively prime

elementary-number-theory divisibility gcd-and-lcm

Prove that there exists a number divisible by 1999 with digit sum 1999

elementary-number-theory divisibility

prove that there are infinitely many numbers of the form $x = 111....1$ such that $31\mid x$

number-theory elementary-number-theory divisibility repunit-numbers

Show that we cannot have a prime triplet of the form $p$, $p + 2$, $p + 4$ for $p >3$

number-theory prime-numbers divisibility

Proving that $ \gcd(a,b) = as + bt $, i.e., $ \gcd $ is a linear combination. [duplicate]

elementary-number-theory divisibility

Understanding the proof of a formula for $p^e\Vert n!$

elementary-number-theory divisibility

If $\gcd (a,b) = 1$, what can be said about $\gcd (a+b,a-b)$? [duplicate]

elementary-number-theory divisibility gcd-and-lcm

Find a counterexample: For every antiprime $n>1$, there is a prime divisor $p$ such that $n/p$ is an antiprime

number-theory elementary-number-theory divisibility examples-counterexamples

Find the largest number that $ n(n^2-1)(5n+2) $ is always divisible by?

elementary-number-theory divisibility

$n^2 + 3n +5$ is not divisible by $121$

number-theory modular-arithmetic divisibility

Functional equation in natural numbers with divisibility: $f(m) + f(n) + mn \ | \ m^2f(m) + n^2f(n) + f(m)f(n)$

elementary-number-theory functions divisibility functional-equations

Proving that any common multiple of two numbers is a multiple of their least common multiple

elementary-number-theory divisibility least-common-multiple

If gcd$(a,b) = 1$, then I want to prove that $\forall c \in \mathbb{Z}$, $ax + by = c$ has a solution in integers $x$ and $y$.

elementary-number-theory divisibility

Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra

elementary-number-theory divisibility totient-function

How can I find integers which satisfy $\frac{150+n}{15+n}=m$?

algebra-precalculus divisibility recreational-mathematics integers

Does $a^n \mid b^n$ imply $a\mid b$?

elementary-number-theory divisibility