Prove $ \frac{1}{x^{2n}}+x^{2n}$ is an integer for all $n$.
123195
Prove by induction that a^n+a^-n is an integer.
86413
Show that $\frac{(m+n-1)!}{m!n!}$ is an integer where m and n are positive integers and gcd(m,n)=1
66578
Prove by induction that $2^{2n} – 1$ is divisible by $3$ whenever n is a positive integer.
26901
induction proof: $\sum_{k=1}^nk^2 = \frac{n(n+1)(2n+1)}{6}$
1125
Inductive proof that ${2n\choose n}=\sum{n\choose i}^2.$
15164
Proof of $\sum^{2N}_{n=1} \frac{(-1)^{n-1}}{n} = \sum^{N}_{n=1} \frac{1}{N+n}$
80144
Prove that $x-1$ divides $x^n-1$
54055
Proof $\prod_{i = 1}^n \frac{n + i}{2i-3} = 2^n(1-2n)$ using inducction
148647
If $\dfrac{4x^2-1}{4x^2-y^2}$ is an integer, then it is $1$
36906
Prove that $x^n+x^{-n} \in \mathbf{N}$ if $x+\frac1x \in \mathbf{N}$
13291
Proving $\sum_{k=1}^n\frac1{\sqrt k}<2\sqrt n$ by induction
32823
Prove $\forall n \in \mathbb{N}: \int_{0}^{\frac{\pi}{2}} |\frac{\sin(nx)}{x}|dx \geq \frac{2}{\pi}\sum_{k=1}^{n}\frac{1}{k}$
37871
Show that, for all $n > 1: \frac{1}{n + 1} < \log(1 + \frac1n) < \frac1n.$
21746
How do I show that the sum $(a+\frac12)^n+(b+\frac12)^n$ is an integer for only finitely many $n$?
26011
To show that $2$ | $x^{2n} - x^n$, $n \in \mathbb{Z^+}$ is the following adequate?
134470
Prove $\frac{k^7}7+\frac{k^5}5+\frac{2k^3}3-\frac k{105}$ is a integer by mathematical induction
144836
How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?