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New posts in divisibility
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
elementary-number-theory
divisibility
gcd-and-lcm
Proving $p\nmid \binom{p^rm}{p^r}$ where $p\nmid m$
algebra-precalculus
number-theory
elementary-number-theory
binomial-coefficients
divisibility
Division by $0$ and its restrictions
algebra-precalculus
divisibility
proof-explanation
rational-numbers
How to prove that $z\gcd(a,b)=\gcd(za,zb)$
abstract-algebra
elementary-number-theory
divisibility
gcd-and-lcm
Theorems related to finding the last digit of large powers of integers [duplicate]
elementary-number-theory
divisibility
$\gcd(a,b)\!=\!1\!=\!\gcd(a,c)\Rightarrow\gcd(a,bc)\!=\!1$ [coprimes to $\,a\,$ are product closed]
elementary-number-theory
divisibility
gcd-and-lcm
Are associates unit multiples in a commutative ring with $1$?
commutative-algebra
ring-theory
divisibility
Prove $\gcd(a+b, a-b) = 1$ or $2\,$ if $\,\gcd(a,b) = 1$
elementary-number-theory
divisibility
gcd-and-lcm
If $n\ne 4$ is composite, then $n$ divides $(n-1)!$.
elementary-number-theory
modular-arithmetic
divisibility
factorial
Extended Euclidean Algorithm: backward vs. forward
divisibility
euclidean-algorithm
If a prime $p\mid ab$, then $p\mid a$ or $p\mid b\ $ [Euclid's Lemma]
elementary-number-theory
prime-numbers
divisibility
How do you explain to a 5th grader why division by zero is meaningless?
divisibility
education
Show that $\gcd\left(\frac{a^n-b^n}{a-b},a-b\right)=\gcd(n d^{n-1},a-b)$
number-theory
elementary-number-theory
divisibility
gcd-and-lcm
Are half of all numbers odd?
divisibility
math-history
parity
Are there four numbers in AP such that their prime factors are also in AP?
sequences-and-series
number-theory
elementary-number-theory
divisibility
recreational-mathematics
The product of $n$ consecutive integers is divisible by $ n!$ (without using the properties of binomial coefficients)
elementary-number-theory
divisibility
factorial
Fibonacci divisibilty properties $ F_n\mid F_{kn},\,$ $\, \gcd(F_n,F_m) = F_{\gcd(n,m)}$
elementary-number-theory
modular-arithmetic
divisibility
fibonacci-numbers
gcd-and-lcm
Prove: If $\gcd(a,b,c)=1$ then there exists $z$ such that $\gcd(az+b,c) = 1$
abstract-algebra
elementary-number-theory
divisibility
gcd-and-lcm
Why polynomial division algorithm works for $x-a$ or any monic polynomial?
abstract-algebra
polynomials
ring-theory
divisibility
Let $a$ and $b$ be non-zero integers, and $c$ be an integer. Let $d = \gcd(a, b)$. Prove that if $a|c$ and $b|c$ then $ab|cd$.
elementary-number-theory
divisibility
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