Newbetuts

Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n [duplicate]

Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?

Is a number meeting these conditions divisible by forty-nine?

How does one show that two general numbers $n! + 1$ and $(n+1)! + 1$ are relatively prime?

Is $\mbox{lcm}(a,b,c)=\mbox{lcm}(\mbox{lcm}(a,b),c)$?

Looking for an example of a GCD domain which is not a UFD

1000! is divisible by 10^n. Find largest value of n [duplicate]

Fastest way to find if a given number is prime

Prove that $b\mid a \implies (n^b-1)\mid (n^a-1)$

Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.

Prove that $\dfrac{(n^2)!}{(n!)^n}$ is an integer for every $n \in \mathbb{N}$

Divisibility Rules for Bases other than $10$

What is the remainder when $1! + 2! + 3! +\cdots+ 1000!$ is divided by $12$?

How many five digit numbers divisible by $3$ can be formed using the digits $0,1,2,3,4,7$ and $8$ if each digit is to be used at most once

Is the number $333{,}333{,}333{,}333{,}333{,}333{,}333{,}333{,}334$ a perfect square?

Proof $\forall n\in\mathbb{N}$, that $9|10^n-1$ by mathematical induction

New posts in divisibility

Prove that if $a$ and $b$ are relatively prime, then $\gcd(a+b, a-b) = 1$ or $2$ [duplicate]

Relationship between Primes and Fibonacci Sequence

Proof by induction that $n^3 + (n + 1)^3 + (n + 2)^3$ is a multiple of $9$. Please mark/grade.

Divisibility of sum of powers: $\ 323\mid 20^n+16^n-3^n-1\ $ for which $n?$

Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n [duplicate]

Let $a,b$ be positive integers such that $a\mid b^2 , b^2\mid a^3 , a^3\mid b^4 \ldots$ so on , then $a=b$?

Is a number meeting these conditions divisible by forty-nine?

How does one show that two general numbers $n! + 1$ and $(n+1)! + 1$ are relatively prime?

Is $\mbox{lcm}(a,b,c)=\mbox{lcm}(\mbox{lcm}(a,b),c)$?

Looking for an example of a GCD domain which is not a UFD

1000! is divisible by 10^n. Find largest value of n [duplicate]

Fastest way to find if a given number is prime

Prove that $b\mid a \implies (n^b-1)\mid (n^a-1)$

Prove that if $n^2$ is divided by 3, then also $n$ can also be divided by 3.

Prove that $\dfrac{(n^2)!}{(n!)^n}$ is an integer for every $n \in \mathbb{N}$

Divisibility Rules for Bases other than $10$

What is the remainder when $1! + 2! + 3! +\cdots+ 1000!$ is divided by $12$?

How many five digit numbers divisible by $3$ can be formed using the digits $0,1,2,3,4,7$ and $8$ if each digit is to be used at most once

Is the number $333{,}333{,}333{,}333{,}333{,}333{,}333{,}333{,}334$ a perfect square?

Proof $\forall n\in\mathbb{N}$, that $9|10^n-1$ by mathematical induction