Prove $\lceil(3 + \sqrt{5})^n\rceil$ is divisible by $2^n$ for all natural numbers $n$
962
divisibility problem using induction
59462
Prove that $n!=\prod_{k=1}^n \operatorname{lcm}(1,2,...,\lfloor n/k \rfloor)$ for any $n \in \mathbb N$
111298
Direct Proof that $1 + 3 + 5 + \cdots+ (2n - 1) = n\cdot n$
11216
Induction: How to prove that $ab^n+cn+d$ is divisible by $m$.
122083
Prove that $\sqrt[3]{2} +\sqrt{5}$ is algebraic over $\mathbb Q$
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
106847
Proof that $n^3+2n$ is divisible by $3$
70951
Prove divisibility law $\,b\mid a,c\,\Rightarrow\, b\mid ka + lc$ for all $k,l\in\Bbb Z$
49299
Proof by Induction: For any integer $n > 0$, $3|(5^{2n} − 1)$.
82774
Prove by mathematical induction that $n^3 - n$ is divisible by $3$ for all natural number $n$
21457
Prove $\sqrt{2\sqrt{3\sqrt{\cdots\sqrt{n}}}}<3$ by induction.
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
74523
Proof by Cases involving divisibility
30620
For which natural n is $3^n+5^n$ divisible by $3^{n-1}+5^{n-1}$?
98946
Prove that $(mn)!$ is divisible by $(n!)\cdot(m!)^n$
95061
Proving that $2^{2\cdot 3^{n-1}}\equiv 1+3^n\pmod{3^{n+1}}$ for every natural $n$
71650
Proving by strong induction for a sequence of integers, $2^n$ divides term $n$