Prove that the number $2^{n}-1$ is divisible by the number $(2^{m}-1)^{2}$ iff the number $n$ is divisible by the number $m(2^{m}-1)$.
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
91921
Divisibility of $n\cdot2^n+1$ by 3.
35052
Prove that if $m^2 + n^2$ is divisible by $4$, then both $m$ and $n$ are even numbers.
2522
Why is $a^n - b^n$ divisible by $a-b$?
49096
How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$
122019
Prove by mathematical induction that $2^{3^n}+1$ is divisible by $3^{n+1}$
5257
Proving that $(3n)!$ is divisible by $n! \times (n + 1)! \times (n + 2)!$ if $n$ is greater than 2
117167
$3^{n+1}$ divides $2^{3^n}+1$
49687
Show that the number 9 divides the number $ m$ if and only if the sum of the digits of the number $ m $ is divisible by 9.
130093
Prove by Induction : $n < 2^n$
79219
Prove that $a^{2^n} \equiv 1 \pmod{2^{n+2}},$ where $a$ is an odd integer.
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
125512
Doubt regarding divisibility of the expression: $1^{101}+2^{101} \cdot \cdot \cdot +2016^{101}$
280
Prove by induction that $5^n - 1$ is divisible by $4$.
52032
Prove that ${n^5 - n}$ is divisible by 5
144132
The number $2^{3^n}+1$ is divisible by $3^{n+1}$ and not divisible by $3^{n+2}$.