How can I prove that $(n^2+11n)/6$ has no remainder?
122711
Prove by induction that $n^3 + 11n$ is divisible by $6$ for every positive integer $n$.
9800
Dividing polynomial $f(x)$ by $x-3$ and $x+6$ leaves respective remainders $7$ and $22$. What's the remainder upon dividing by $(x-3)(x+6)$?
79652
Proof by induction that $2 + 4 + 6 + \cdots + 2n = n(n+1)$
25299
What is the remainder when $2^{1990}$ is divided by $1990$?
137808
$n^2 + 3n +5$ is not divisible by $121$
117999
Prove by contradiction (not using a calculator) that $\sqrt6 + \sqrt2 < \sqrt{15}$?
24053
How can I prove that $n^7 - n$ is divisible by $42$ for any integer $n$?
6160
How to prove a number $a$ is quadratic residue modulo $n$?
102420
How to prove that adding $n$ to the numerator and denominator will move the resultant fraction close to $1$?
126312
How can you prove $\binom {2n}{2} = 2\binom{n}{2} + n^2$?
139776
Divisibility tests and remainder mod $9,11,99,101,999,1001\,$ (casting out nines and elevens)
69902
$3$ never divides $n^2+1$
4475
Find the remainder when $2^{2016}$ is divided by $47$
26301
Prove that $x^3 \equiv x \bmod 6$ for all integers $x$
25023
How do you prove that there are infinitely many primes of the form $5 + 6n$?
113506
negative number divided by positive number, what would be remainder?
28957
Verifying that $2^{44}-1$ is divisible by $89$