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New posts in divisibility
highest power of prime $p$ dividing $\binom{m+n}{n}$
elementary-number-theory
binomial-coefficients
divisibility
Suppose $(a,b)=1$, then $(2a+b,a+2b)=1\text{ or }3$.
elementary-number-theory
divisibility
gcd-and-lcm
One of any consecutive integers is coprime to the rest
elementary-number-theory
prime-numbers
divisibility
gcd-and-lcm
How could I find $x$ in this equation $x^2-x+6 \equiv 0 \pmod {9}$
modular-arithmetic
divisibility
quadratics
If $\gcd(a,b)=d$, then $\gcd(ac,bc)=cd$?
number-theory
divisibility
gcd-and-lcm
Why does $a^n - b^n$ never divide $a^n + b^n$?
elementary-number-theory
divisibility
Notation for "is divisible by"
elementary-number-theory
notation
divisibility
Prove if $56x = 65y$ then $x + y$ is divisible by $11$
proof-writing
divisibility
An enigmatic pattern in division graphs
elementary-number-theory
divisibility
visualization
How to prove that $\frac{(5m)!(5n)!}{(m!)(n!)(3m+n)!(3n+m)!}$ is a natural number?
elementary-number-theory
inequality
contest-math
divisibility
ceiling-and-floor-functions
If $n\in\mathbb N$ and $4^n+2^n+1$ is prime, prove that there exists an $m\in\mathbb N\cup\{0\}$ such that $n=3^m$.
elementary-number-theory
divisibility
Is there a prime every year if YYYYMMDD is treated as a base-$10$ number?
number-theory
elementary-number-theory
prime-numbers
divisibility
recreational-mathematics
How to solve this algorithmic math olympiad problem?
sequences-and-series
elementary-number-theory
algorithms
divisibility
There is a number divisible by all integers from 1 to 200, except for two consecutive numbers. What are the two?
elementary-number-theory
prime-numbers
divisibility
gcd-and-lcm
$a\mid b,c\mid d\Rightarrow\,\gcd(a,c)\mid \gcd(b,d)$
elementary-number-theory
divisibility
gcd-and-lcm
Prove that $6|2n^3+3n^2+n$
elementary-number-theory
divisibility
If $\gcd(a,c)=1=\gcd(b,c)$, then $\gcd(ab,c)=1$ [duplicate]
elementary-number-theory
divisibility
gcd-and-lcm
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
elementary-number-theory
induction
divisibility
Conjectured analogue of Fermat's Little Theorem for Bernouli numbers
number-theory
elementary-number-theory
prime-numbers
divisibility
bernoulli-numbers
Primes $p$ such that $p^2$ divides $x^2 + y^2 + 1$
number-theory
elementary-number-theory
prime-numbers
divisibility
problem-solving
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