Show that $n^5-n$ is divisible by 80 given that n is an odd integer greater than 1.
99908
When does $120$ divide $n^5 - n$
40565
How can I prove that one of $n$, $n+2$, and $n+4$ must be divisible by three, for any $n\in\mathbb{N}$
116363
If $P(x^5)+xQ(x^5)+x^2R(x^5)=(x^4+x^3+x^2+x+1)S(x)$ , then prove that $P(x)$ is divisible by $x-1$
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 $3$
49096
How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$
15631
Show that $11^{n+1}+12^{2n-1}$ is divisible by $133$.
97805
$n+1$ is a divisor of $\binom{2n} {n}$
1837
Showing that $1^k+2^k + \dots + n^k$ is divisible by $n(n+1)\over 2$
68561
How to show $\lceil ( \sqrt3 +1)^{2n}\rceil$ where $n \in \mathbb{ N}$ is divisible by $2^{n+1}$
27063
Prove that if n is an odd positive integer , then $n^2\equiv1\mod8$
33866
Show that $n$ does not divide $2^n - 1$ where $n$ is an integer greater than $1$?
65430
Using the Well Ordering Principle to Show that n^3 - n is divisible by 6.
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
26588
Prove by induction that $10^n -1$ is divisible by 11 for every even natural number
98963
Prove that neither $A$ nor $B$ is divisible by $5$