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New posts in divisibility
Coprime cofactors of n'th powers are n'th powers, up to associates, for Gaussian integers & UFD
algebraic-number-theory
divisibility
Prove that $n^3(n^2-1)$ is divisible by 24 for all n
elementary-number-theory
polynomials
induction
divisibility
Fibonacci sequence divisible by 7?
combinatorics
elementary-number-theory
divisibility
fibonacci-numbers
How does the divisibility graphs work?
elementary-number-theory
graph-theory
recreational-mathematics
divisibility
Prove $a+b+c+d $ is composite
elementary-number-theory
prime-numbers
contest-math
divisibility
Show that $n^3-n$ is divisible by $6$ using induction
induction
divisibility
Divisor of a product of integers is a product of divisors
elementary-number-theory
divisibility
gcd-and-lcm
Greatest common divisor is the smallest positive number that can be written as $sa+tb$
elementary-number-theory
divisibility
gcd-and-lcm
For integers $a$ and $b$, $ab=\text{lcm}(a,b)\cdot\text{hcf}(a,b)$
elementary-number-theory
divisibility
gcd-and-lcm
least-common-multiple
GCD Proof with Multiplication: gcd(ax,bx) = x$\cdot$gcd(a,b)
elementary-number-theory
divisibility
gcd-and-lcm
Concise proof that every common divisor divides GCD without Bezout's identity?
number-theory
elementary-number-theory
divisibility
gcd-and-lcm
least-common-multiple
Find $a,b \in \mathbb{N}$ with $\mathrm{lcm}(a,b)=12\gcd(a,b)\,$ and $\,a\bmod b = 5$
elementary-number-theory
divisibility
$b \mid ac\Rightarrow b \mid (a,b)(c,b)\,$ for integers $\,a,b,c$
elementary-number-theory
divisibility
gcd-and-lcm
Has there ever been an application of dividing by $0$?
divisibility
axioms
How to show $a^{2^n}+1 \mid a^{2^m}-1$?
elementary-number-theory
divisibility
$\gcd(b^x - 1, b^y - 1, b^ z- 1,\dots) = b^{\gcd(x, y, z,\dots)} -1$ [duplicate]
elementary-number-theory
divisibility
gcd-and-lcm
perfect-powers
Prove $n-m \mid n^r - m^r\,$ [Factor Theorem, monomial case]
algebra-precalculus
modular-arithmetic
induction
divisibility
Prove: If $a\mid m$ and $b\mid m$ and $\gcd(a,b)=1$ then $ab\mid m$
elementary-number-theory
divisibility
gcd-and-lcm
How to prove $n^5 - n$ is divisible by $30$ without reduction
elementary-number-theory
divisibility
How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
elementary-number-theory
divisibility
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