If $n$ is an even natural number then $2^{n-1}$ is divisible for $2^{\varphi(n)}$?
58663
How to show that if $\phi(n)$ equals to n itself, then n must be 1?
151692
When does $2^n-1$ divide $3^n-1$?
110695
Divisor of $2^{2^n} + 1$ modulus $2^{n+1}$
35553
If $n$ is composite, so is $2^n-1$
52032
Prove that ${n^5 - n}$ is divisible by 5
33757
For what natural numbers is $n^3 < 2^n$? Prove by induction
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
116970
On the number divisors of a number
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
96341
Proving $v(s,p)=2^{p-1}(2s-1)$ is a bijection of natural numbers and $f(s)=2s-1$ is a bijection between natural numbers and odd numbers.
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
9997
For what powers $k$ is the polynomial $n^k-1$ divisible by $(n-1)^2$?
94983
Can an odd number $n$ divide $2^n-1$?
83036
f(g(x)) has a degree divisible by n
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.