Let $n$ be a positive integer. A pair of $n$-tuples $(a_1,....a_n)$ and $(b_1,...b_n)$ with integer entries is called an exquisite pair if
$|a_1b_1 +...+ a_nb_n| \leq 1$.
Determine the maximum number of distinct $n$-tuples with integer entries such that any two of them form an exquisite pair.
APMO 2017 P5
The study of mathematics, like the Nile, begins in minuteness but ends in magnificence.
- Charles Caleb Colton
- Charles Caleb Colton