Newbetuts

How come the number $N!$ can terminate in exactly $1,2,3,4,$ or $6$ zeroes but never $5$ zeroes? [duplicate]

Prove with induction that $11$ divides $10^{2n}-1$ for all natural numbers.

Proving $364 \mid n^{91} - n^7$ [Generalization of Euler & Fermat Theorems]

Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$

Find the values of $n$ that make the fraction $\frac{2n^{7}+1}{3n^{3}+2}$ reducible.

Prove 24 divides $u^3-u$ for all odd natural numbers $u$

In arbitrary commutative rings, what is the accepted definition of "associates"?

If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$

For what powers $k$ is the polynomial $n^k-1$ divisible by $(n-1)^2$? [closed]

If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.

How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$

Show that $11^{n+1}+12^{2n-1}$ is divisible by $133$.

Fractals using just modulo operation

Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds]

What is the smallest positive multiple of 450 whose digits are all zeroes and ones?

New posts in divisibility

Show that $a^n \mid b^n$ implies $a \mid b$

Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$

$\gcd\left(a+b,\frac{a^p+b^p}{a+b}\right)=1$, or $p$

$n \mid (a^{n}-b^{n}) \ \Longrightarrow$ $n \mid \frac{a^{n}-b^{n}}{a-b}$

Prove $n\mid \phi(2^n-1)$

How come the number $N!$ can terminate in exactly $1,2,3,4,$ or $6$ zeroes but never $5$ zeroes? [duplicate]

Prove with induction that $11$ divides $10^{2n}-1$ for all natural numbers.

Proving $364 \mid n^{91} - n^7$ [Generalization of Euler & Fermat Theorems]

Find $x,y$ given $\gcd(x,y)$ and ${\rm lcm}(x,y)$

Find the values of $n$ that make the fraction $\frac{2n^{7}+1}{3n^{3}+2}$ reducible.

Prove 24 divides $u^3-u$ for all odd natural numbers $u$

In arbitrary commutative rings, what is the accepted definition of "associates"?

If $\gcd(a, b) = 1$, then $\gcd(ab, c) = \gcd(a, c) \cdot\gcd(b, c)$

For what powers $k$ is the polynomial $n^k-1$ divisible by $(n-1)^2$? [closed]

If $\gcd(a,b)=1$, then $\gcd(a+b,a^2 -ab+b^2)=1$ or $3$.

How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$

Show that $11^{n+1}+12^{2n-1}$ is divisible by $133$.

Fractals using just modulo operation

Why is $\gcd(x^4+1,x^2-1) = 1$ but I get $2$? [unit normalization of gcds]

What is the smallest positive multiple of 450 whose digits are all zeroes and ones?