What is the largest $n$ for which $n+5$ divides $n^5+5$
62043
the largest integer $n$ for which $n+5$ divivides $n^5+5$?
83634
Find $\lim_{n\to \infty}\sqrt[n]{3^n+5^n}$
5206
Highest power of a prime $p$ dividing $N!$
18405
What is the greatest integer that divides $p^4-1$ for every prime number $p$ greater than $5$?
152577
Proving $4^n > n^4$ holds for $n\geq 5$ via induction.
142347
What is the highest power of $n$ in $(n^r-1)!$
157914
$13$ is the largest prime that can divide two successive integers of the form $n^2+3$
48875
$n^3 \equiv n^5 \pmod{12} $?
117969
Suppose $n$ divides $3^n + 4^n$. Show that $7$ divides $n$.
77076
Proof that $(x-1)^2$ divides a $nx^{n+1} – (n+1)x^{n}+1$
21439
For which $k\in \Bbb N$ does $x^2+x+1$ divide $ (x + 1)^{2k}+x^{2k} + 1$?
80144
Prove that $x-1$ divides $x^n-1$
63383
Integers $n$ for which $|2^n + 5^n – 65|$ is a perfect square
83935
Using congruences, show $\frac{1}{5}n^5 + \frac{1}{3}n^3 + \frac{7}{15}n$ is integer for every $n$
17751
Find the greatest value of $\arg z$ achieved on a circle in $\mathbb{C}$
90806
Find all positive integers $n$ such that $n$ is divisible by all the positive integers less than or equal to $\sqrt{n}$
50670
Use Mathematical Induction to prove 6 divides $n(n+1)(2n+1)$