Prove if $(x+1/x)$ is an integer then $(x^n+1/x^n)$ is an integer
49372
$x+1/x$ an integer implies $x^n+1/x^n$ an integer
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
67527
Proof by Induction that $3^n ≥ 1+2^n$
63409
If $x^2+ax+b=0$ has a rational root, show that it is in fact an integer
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
45645
Using permutation or otherwise, prove that $\frac{(n^2)!}{(n!)^n}$ is an integer,where $n$ is a positive integer.
12967
Find all $n>1$ such that $\dfrac{2^n+1}{n^2}$ is an integer.
99052
Prove that $( 1 + n^{-2}) ^n \to 1$.
43246
Showing that if $a<b$, then $a^{1/n} < b^{1/n}$
150088
Prove that $\sqrt {n − 1} +\sqrt {n + 1}$ is irrational for every integer $n ≥ 1$
83935
Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
127183
Proof: For all integers $x$ and $y$, if $x^3+x = y^3+y$ then $x = y$
50927
If $m,n\in N$ Prove that there is such a positive integer k, such that $(\sqrt{m}+\sqrt{m+1})^n=\sqrt{k}+\sqrt{k+1}$
44897
Proof: If $n=ab$ then $2^a-1 \mid 2^n-1$
27281
How to prove $\,x^a-1 \mid x^b-1 \iff a\mid b$
62613
Need to proof by induction (calculus1 n and n+1)