Question 1
Fix positive integers $k$ and $d$.
Prove that for all sufficiently large odd positive integers $n$,
the digits of the base-$2n$ representation of $n^k$ are all greater than $d$.
Proposed by John Berman.
Manual essay; 1 editorial point, not official contest scoring. Automatic answer fields are intentionally empty.
Prove that for all sufficiently large odd positive integers $n$,
the digits of the base-$2n$ representation of $n^k$ are all greater than $d$.
Proposed by John Berman.
Manual essay; 1 editorial point, not official contest scoring. Automatic answer fields are intentionally empty.