Newbetuts

Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$

Writing a GCD of two numbers as a linear combination

Set of $n$ natural numbers {$a_i$} such that: if $a_j\lt a_k$, then $(a_k-a_j)\mid a_j$

How many 0's are in the end of this expansion?

Showing $\gcd(n!i+1,n!j+1) = 1$ for $n \in \mathbb{N}$ if $i$ and $j$ are integers with $1\leq i < j \leq n$

How many positive divisors $X = 2^2 \cdot 3^3 \cdot 4^4 \cdot 5^5 \cdot6^6 \cdot 7^7$ are divisible by $35$?

What is $\underbrace{555\cdots555}_{1000\ \text{times}} \ \text{mod} \ 7$ without a calculator

Proof by Contradiction - two distinct primes not divisible by each other

Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.

Is $x!-(x-1)!-(x-2)!-...-1!$ always divisible by three?

How does one attack a divisibility problem like $(a+b)^2 \mid (2a^3+6a^2b+1)$?

Show that among any consecutive $16$ natural numbers one is coprime to all others

$ 0 < a < b\,\Rightarrow\, b\bmod p\, <\, a\bmod p\ $ for some prime $p$

Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?

New posts in divisibility

How many numbers $n$ are there such that $\gcd(n,\phi(n)) = 1$?

Which number has the highest divisibility (factors)?

How to prove that for all $m,n\in\mathbb N$, $\ 56786730 \mid mn(m^{60}-n^{60})$? [duplicate]

Show that $(n!)^{(n-1)!}$ divides $(n!)!$ [duplicate]

LCM of First N Natural Numbers

Why would some elementary number theory notes exclude 0|0?

Solutions to $a,\ b,\ c,\ \frac{a}{b}+\frac{b}{c}+\frac{c}{a},\ \frac{b}{a} + \frac{c}{b} + \frac{a}{c} \in \mathbb{Z}$

Writing a GCD of two numbers as a linear combination

Set of $n$ natural numbers {$a_i$} such that: if $a_j\lt a_k$, then $(a_k-a_j)\mid a_j$

How many 0's are in the end of this expansion?

Showing $\gcd(n!i+1,n!j+1) = 1$ for $n \in \mathbb{N}$ if $i$ and $j$ are integers with $1\leq i < j \leq n$

How many positive divisors $X = 2^2 \cdot 3^3 \cdot 4^4 \cdot 5^5 \cdot6^6 \cdot 7^7$ are divisible by $35$?

What is $\underbrace{555\cdots555}_{1000\ \text{times}} \ \text{mod} \ 7$ without a calculator

Proof by Contradiction - two distinct primes not divisible by each other

Prove that if $3\mid a^2+b^2$ then $3\mid a$ and $3\mid b$.

Is $x!-(x-1)!-(x-2)!-...-1!$ always divisible by three?

How does one attack a divisibility problem like $(a+b)^2 \mid (2a^3+6a^2b+1)$?

Show that among any consecutive $16$ natural numbers one is coprime to all others

$ 0 < a < b\,\Rightarrow\, b\bmod p\, <\, a\bmod p\ $ for some prime $p$

Does $n \mid 2^{2^n+1}+1$ imply $n \mid 2^{2^{2^n+1}+1}+1$?