Show that $a_n=\frac{1}{2}+\frac{1}{3}+...+\frac{1}{n}$ would not contain a natural number for all n
46946
Is there an elementary proof that $\sum \limits_{k=1}^n \frac1k$ is never an integer?
33757
For what natural numbers is $n^3 < 2^n$? Prove by induction
33705
Is $0$ a natural number?
43939
Show that $3^{2n+1}-4^{n+1}+6^n$ is never prime for natural n except 1.
70561
limit of the sequence $a_n=1+\frac{1}{a_{n-1}}$ and $a_1=1$
14435
Show by induction: $(1+\frac{1}{n})^{n}<n$
25054
Proving $\frac{1}{n+1} + \frac{1}{n+2}+\cdots+\frac{1}{2n} > \frac{13}{24}$ for $n>1,n\in\Bbb N$ by Induction
4530
For which natural numbers are $\phi(n)=2$?
28942
About Math notation: the set of the first $n$ natural numbers
123427
Proving the sum of the first $n$ natural numbers by induction
52672
Solution of $\frac{a}{b}=\frac{a'}{b'}$ if $a,b,a',b' \in \mathbb{N}$
145519
Prove that for any natural number $n>1$, we have $(2n)!<(n(n+1))^n$
102738
Show that $e^n>\frac{(n+1)^n}{n!}$ without using induction.
129693
An interesting problem with "decomposing" natural numbers.
128415
Prove that $1<\frac{1}{1001}+\frac{1}{1002}+\frac{1}{1003}+\dots+\frac{1}{3001}<\frac43$
72600
Proof that $n!\leq {(\frac{n+1}{2})}^{n}$
113695
Show that there is no integer n with $\phi(n)$ = 14