Prove that $9^{n+1} - 8n- 9$ divisible by $64$
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
105854
Prove $n^2(n^4-1)$ is divisible by 60 using Mathematical Induction.
2522
Why is $a^n - b^n$ divisible by $a-b$?
91921
Divisibility of $n\cdot2^n+1$ by 3.
122878
How can I prove that $2/9<x^4+y^4<8$?
81601
Prove that if $x$ is odd then $x^2 -1$ is divisible by $8$.
144447
Show that $504 \mid (n^9 − n^3 )$ for any integer $n$
124685
How to show $(mn)!$ is divisible by $(m!)^n$?
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
63416
Prove $(n^5-n)$ is divisible by 5 by induction.
79940
$\binom{p}{i}$ divisible by $p$, with $p$ prime
112147
Proving $9$ divides $n^3 + (n+1)^3 + (n+2)^3$
26336
Prove that $n(n^2 - 1)(n + 2)$ is divisible by $4$ for any integer $n$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
116970
On the number divisors of a number
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.