Prove that $133$ divides $11^{n+1} + 12^{2n−1}$ for all $n > 1$?
15631
Show that $11^{n+1}+12^{2n-1}$ is divisible by $133$.
80144
Prove that $x-1$ divides $x^n-1$
48053
Show that 13 divides $2^{70}+3^{70}$
100558
Prove that for any even positive integer $n$, $n^2-1 \mid 2^{n!}-1$
100305
Prove $2^n-1$ is divisible by $(2^m-1)^2$ iff...
66623
Primes dividing $11, 111, 1111, ...$
124816
Using the fact that $n^3 + 5n$ is divisible by $6$, infer that $n^4 - 2n^3 + 11n^2 + 14n$ is always divisible by $24$
48333
Prove by induction that $(x+1)^n - nx - 1$ is divisible by $x^2$
127833
Proving that $7^n(3n+1)-1$ is divisible by 9
122386
How do I prove that $3$ divides $14^{2n}-1$ by induction?
32166
Prove: if $n\mid 7^n+6^n$ and $n>1$, then $13\mid n$
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
139776
Divisibility tests and remainder mod $9,11,99,101,999,1001\,$ (casting out nines and elevens)
94983
Can an odd number $n$ divide $2^n-1$?
157294
Prove that if $n>1$ is odd, then $1^n+2^n+3^n+\ldots+(n-1)^n$ is divisible by $n$
77816
Proof problem: Show that $n^2-1$ is divisible by $8$, if $n$ is an odd positive integer.
48875
$n^3 \equiv n^5 \pmod{12} $?