Prove that $n^4−1 $ is divisible by 5 when n is not divisible by 5.
107725
Prove that if $n$ is not divisible by $5$, then $n^4 \equiv 1 \pmod{5}$
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
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 $x-1$
6561
Prove that the expression $5^{2n+1} \cdot 2^{n+2} + 3^{n+2} \cdot 2^{2n+1}$ is divisible by 19.
105854
Prove $n^2(n^4-1)$ is divisible by 60 using Mathematical Induction.
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
10629
How to prove $4(n!)>2^{n+2}$ for $ n\geq 4$ with induction
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
113359
Proving that $x^2 + 4$ is not divisible by $3$
134149
$z^n=(z+1)^n=1$, show that $n$ is divisible by $6$.
49096
How can I prove $5^{3^n}+1$ is divisible by $3^{n+1}$
19701
Prove $5\mid2^{4n}-1$ by induction
4077
Using induction prove $n^3-n$ is divisible by 3 whenever n is a positive number.
114873
Show that if $n$ is not divisible by $2$ or by $3$, then $n^2-1$ is divisible by $24$.
280
Prove by induction that $5^n - 1$ is divisible by $4$.
10191
Binomial theorem: divisibility by $n^2$