Prove that $n^5+n^4+1$ is composite for $n>1.$
124869
Prime factor of $A=14^7+14^2+1$
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
96332
Prove by induction that $\sqrt[n+1]{n+1}<\sqrt[n]{n}$ for $n\ge 3$
65757
Prove that $n! + k$ is a composite number
17714
Proof $\sum_{k=1}^n (-1)^{k+1} \binom{n}{k}\frac{1}{k} = H_n$ by induction
55266
Prove that $(n+1)^{n-1}<n^n$
150642
How to prove $\sum^n_{i=1} \frac{1}{i(i+1)} = \frac{n}{n+1}$?
158563
If $m^4+4^n$ is prime, then $m=n=1$ or $m$ is odd and $n$ even
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
46102
Prove that $2^n +1$ in never a perfect cube
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
70981
Galois Group of $x^5+1$
100375
Prove that ${\sqrt {n} }^{\sqrt {n+1}} > {\sqrt {n+1}}^{\sqrt {n}}$.
83738
Prove $(k,n+k)=1$ iff $(k,n)=1$
33082
Proving $\sum_{i=0}^n 2^i=2^{n+1}-1$ by induction.
88880
Induction Proof $4^k < 5^k$