How to prove that $4^n-3n-1$ is divisible by 9?
12729
Proving $9^n - 8n - 1$ is divisible by $8^2$ for $n\ge 0$?
10744
Prove that a number is divisible by 3 iff the sum of its digits is divisible by 3
150462
Prove by induction that for every $n \ge 0$ the term $2^{2n+1} - 9n^2 + 3n -2$ is divisible by $54$
139776
Divisibility tests and remainder mod $9,11,99,101,999,1001\,$ (casting out nines and elevens)
113359
Proving that $x^2 + 4$ is not divisible by $3$
97947
How can we prove that a binomial coefficient $n\choose m$is divisible by the ratio of $n$ and $\gcd(n,m)$?
62100
Show that $n^3-n$ is divisible by $6$ using induction
31344
Proving $2^{2^n}+3^{2^n}+5^{2^n}$ is divisible by $19$ for all $n\geq 1$ by induction
280
Prove by induction that $5^n - 1$ is divisible by $4$.
34784
Is a number meeting these conditions divisible by forty-nine?
108382
Prove $x^n-1$ is divisible by $x-1$ by induction
144447
Show that $504 \mid (n^9 − n^3 )$ for any integer $n$
87379
How to prove that $2^{n+2}+3^{2n+1}$ is divisible by 7 using induction?
80144
Prove that $x-1$ divides $x^n-1$
85941
Proof by induction that $n^3 - n$ is divisible by $6$
49687
Show that the number 9 divides the number $ m$ if and only if the sum of the digits of the number $ m $ is divisible by 9.
52032
Prove that ${n^5 - n}$ is divisible by 5