Show that $30$ is a divisor of $n^5-n$ for all positive integers
3611
How to prove $n^5 - n$ is divisible by $30$ without reduction
134739
product of divisors of n as a power of n.
52800
Show that $z^5-1=(z-1)(z^2+2z\cos{\pi \over 5}+1)(z^2-2z\cos{2\pi \over 5}+1)$
24053
How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
116970
On the number divisors of a number
19701
Prove $5\mid2^{4n}-1$ by induction
109532
Proving $5^n \equiv 1 \pmod {2^r}$ when $n=2^{r-2}$
49096
How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$
91451
find all positive integer $m,n$
112120
Find all primes of the form $2^{2^n} + 5$ for a nonnegative integer n
19046
Show that if $a$ and $b$ are positive integers with $(a,b)=1$ then $(a^n, b^n) = 1$ for all positive integers n
139269
Prove that $2n-3\leq 2^{n-2}$ , for all $n \geq 5$ by mathematical induction
59479
For a positive integer $n\geq 2$ with divisors $1=d_1<d_2<\cdots<d_k=n$, prove that $d_1d_2+d_2d_3+\cdots+d_{k-1}d_k<n^2$
75516
Relatively Prime Numbers and Number of Divisors of n
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
110444
Finding out the number of divisors
66016
Prove $3^{2n+1} + 2^{n+2}$ is divisible by $7$ for all $n\ge0$