Show that $30$ divides $n^{5} - n$, where n is an integer
52032
Prove that ${n^5 - n}$ is divisible by 5
117167
$3^{n+1}$ divides $2^{3^n}+1$
69039
Prove that $2730$ divides $n^{13} - n$ for all integers $n$.
117969
Suppose $n$ divides $3^n + 4^n$. Show that $7$ divides $n$.
55437
When does $2^{n}$ divide $3^{n}-1$
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
105854
Prove $n^2(n^4-1)$ is divisible by 60 using Mathematical Induction.
152577
Proving $4^n > n^4$ holds for $n\geq 5$ via induction.
122577
Prove that $(n^3 - 1)n^3(n^3 + 1)$ is divisible by $504$
116054
The number $(3+\sqrt{5})^n+(3-\sqrt{5})^n$ is an integer
133017
Prove that $n^n>1\times3\times5\times7\times \dots\times(2n-1)$
23684
Prove for all integer $n > 1$ that if $n | 34$, then $n+5$ and $n^2+$9 are coprime
48875
$n^3 \equiv n^5 \pmod{12} $?
10589
How to factorize $5$ in $\mathbb{Z}[\root 3 \of 2]$?
147101
Show that if $p>5$ is prime, then $240 \mid (p^4-1)$
27798
Prove that $ n^3 + 5n$ is divisible by 6 for all $n\in \textbf{N}$
151025
If G is a group of order n=35, then it is cyclic