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New posts in divisibility
Is there an Integral domain that is a GCD domain but NOT a UFD? [duplicate]
commutative-algebra
divisibility
integral-domain
unique-factorization-domains
gcd-and-lcm
Prove that neither $A$ nor $B$ is divisible by $5$
number-theory
elementary-number-theory
divisibility
harmonic-numbers
Is an arbitrary number of the form xyzxyz divisible by 7, 11, 13?
elementary-number-theory
discrete-mathematics
prime-numbers
divisibility
Show that any two consecutive odd integers are relatively prime
elementary-number-theory
divisibility
gcd-and-lcm
What is the density of squarefree numbers in $p+n$ for prime $p$ and natural $n$?
number-theory
elementary-number-theory
prime-numbers
divisibility
analytic-number-theory
Divisibility of prime numbers
discrete-mathematics
prime-numbers
divisibility
Let $a\mid c$ and $b\mid c$ such that $\gcd(a,b)=1$, Show that $ab\mid c$
elementary-number-theory
divisibility
gcd-and-lcm
$\textit{Why}$ the cases in 4 $\nmid n^2 - 3?$ (bases cases in modular induction)
proof-explanation
divisibility
If $f$ divides $g$ in $S[x]$, show that $f$ divides $g$ in $R[x]$ for $R$ a sub-ring of $S$.
abstract-algebra
polynomials
ring-theory
divisibility
Are the polynomial remainder and factor theorems equivalent?
abstract-algebra
polynomials
divisibility
If $(a,b) = 1$ then $a,b|n \implies ab|n$
elementary-number-theory
divisibility
For natural numbers $a$ and $b$, show that $a \Bbb Z + b \Bbb Z = \gcd(a, b)\Bbb Z $ [duplicate]
abstract-algebra
elementary-number-theory
divisibility
gcd-and-lcm
$(a^{n},b^{n})=(a,b)^{n}$ and $[a^{n},b^{n}]=[a,b]^{n}$?
elementary-number-theory
prime-numbers
divisibility
Divisibility by $9$
elementary-number-theory
divisibility
decimal-expansion
Is the smallest non-1 divisor of a number always prime?
elementary-number-theory
prime-numbers
divisibility
Find all the natural numbers between $1 \leq a \leq 1000$ which fulfill $a^{11764} \equiv a^4\pmod{25725}$ [duplicate]
elementary-number-theory
modular-arithmetic
divisibility
Is $\sum_{k=1}^{n} k^k / \sum_{k=1}^{n} k \in \mathbb{N}$ for some $n > 1$?
number-theory
recreational-mathematics
divisibility
problem-solving
$a^n-a + 1 $ divisible by $n$
number-theory
elementary-number-theory
divisibility
Is every prime is the largest prime factor in some prime gap?
number-theory
elementary-number-theory
prime-numbers
divisibility
analytic-number-theory
show that if $a | c$ and $b | c$, then $ab | c$ when $a$ is coprime to $b$.
elementary-number-theory
divisibility
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