Prove that $7^n - 1$ is divisible by 6
31292
Divisibility Proof with Induction - Stuck on Induction Step
145889
Prove if $56x = 65y$ then $x + y$ is divisible by $11$
112631
Prove that if $d$ divides $n$, then $2^d -1$ divides $2^n -1$
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
50940
Prove $1^{2007}+2^{2007}+\cdots+n^{2007}$ is not divisible by $n+2$
50670
Use Mathematical Induction to prove 6 divides $n(n+1)(2n+1)$
2522
Why is $a^n - b^n$ divisible by $a-b$?
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
121706
Show $\text{det}(A)$ is divisible by $2^{n-1}$
126888
How can you show that $\binom {n}{7}=\sum_{k=7}^n \binom {k-1} {6}$?
74523
Proof by Cases involving divisibility
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
280
Prove by induction that $5^n - 1$ is divisible by $4$.
56760
Prove by induction that an expression is divisible by 11
52644
Prove $2^k+1$ divisible by 3 for odd K
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$