Prove $4^{n} -1$ is divisible by $3$ for all $n\geq1$
2522
Why is $a^n - b^n$ divisible by $a-b$?
96268
Prove that $5$ divides $3^{3n+1}+2^{n+1}$
95889
Prove that $\gcd(n! + 1, 3n! + 1) = 1$, $\forall n \in \mathbb{N}$, $n \geq 2$.
145891
Prove that $n! > \sqrt{n^n}, n \geq 3$
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
26912
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
91197
Proving $n! \ge 2^{n-1 }$for all $n\ge1 $by mathematical Induction
113359
Proving that $x^2 + 4$ is not divisible by $3$
33011
Prove that the polynomial $f_n(x)=nx^{n+1}-(n+1)x^n+1$ is divisible by $(x-1)^2$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
125618
Prove $2^{3^n}+1 $ is a multiple of $3^{n+1}$ by induction
125855
Prove: The product of any three consecutive integers is divisible by $6$.
153281
Prove by induction that $3^{2n+3}+40n-27$ is divisible by 64 for all n in natural numbers
27147
Proving $n! > n^3$ for all $n > a$
117969
Suppose $n$ divides $3^n + 4^n$. Show that $7$ divides $n$.
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
150462
Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$