Suppose $n$ divides $3^n + 4^n$. Show that $7$ divides $n$.
32166
Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$
75373
Show that $2^n>n$ for $n\in \mathbb{N}$
21100
Simple Proof by induction: $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
126816
Question of remainder on dividing by 7
65280
If $a, b, c >0$ prove that $ [(1+a)(1+b)(1+c)]^7 > 7^7a^4b^4c^4 $.
27798
Prove that $ n^3 + 5n$ is divisible by 6 for all $n\in \textbf{N}$
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
18693
If $a,b$ are positive integers such that $a^{n}+n$ divides $b^{n}+n$ for every $n$, then $a=b$
80365
Prove that $n$ is divisible by $6$
46741
Prove that $n$ divides $\phi(a^n -1)$ where $a, n$ are positive integer without using concepts of abstract algebra
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
125040
Show by induction : $n^7-n$ is a multiple of 7
50670
Use Mathematical Induction to prove 6 divides $n(n+1)(2n+1)$
29963
$6$ divides $a+b+c$ if and only if $6$ divides $a^{3}+b^{3}+c^{3}$
71650
Proving by strong induction for a sequence of integers, $2^n$ divides term $n$