Question 5
Find all positive integers $k$ such that: for every positive integer $n$, the sum
$$\binom n0^k + \binom n1^k + \dots + \binom nn^k$$
is divisible by $n+1$.
Proposed by John Berman.
Manual essay; 1 editorial point, not official contest scoring. Automatic answer fields are intentionally empty.
$$\binom n0^k + \binom n1^k + \dots + \binom nn^k$$
is divisible by $n+1$.
Proposed by John Berman.
Manual essay; 1 editorial point, not official contest scoring. Automatic answer fields are intentionally empty.