Find the function $f(k)$, $k > 1$ that is the largest integer and is a divisor of $n^k - n$ for all integers $n$.
69039
Prove that $2730$ divides $n^{13} - n$ for all integers $n$.
83036
f(g(x)) has a degree divisible by n
69876
For every $n \in \mathbb{N}$, find a function $f$ which is differentiable $n$ times at $0$, but not $n+1$ times.
19459
Find remainder of $F_n$ when divided by $5$
102733
What is the largest number $n$ with $\lambda(n)=k$ for a given $k$?
28286
About finding the function such that $f(xy)=f(x)f(y)-f(x+y)+1$
96861
How find all ordered pairs $(m,n)$ such $\frac{n^3-1}{mn-1}$ is an integer
124241
Finding all integers $k \geq 2$ such that $k^2 \equiv 5k \pmod{15}$. What is going on here?
10191
Binomial theorem: divisibility by $n^2$
95694
Is there a name for the function $\max(x, 0)$?
85535
Finding maximum of $|f'(i)|$
50552
find functions that $f(m+k)=f(mk-n)$
55693
The functional equation $ f \big( x - f ( y ) \big) = f \big( f ( y ) \big) + x f ( y ) + f ( x ) - 1 $
31698
$f(m^2 + f(n)) = f(m)^2 + n$ for all natural numbers
134439
Proving function is $C^k$
132488
Find all entire functions $f(z)$ such that $|f(z)|=1$ for $|z|=1$
20478
Mathematical expression for $n$ largest values in a set