Terms overload
Algebra
Level
5
Real numbers \( a_1, a_2, \ldots, a_{80090} \) satisfy
\[ (a_1 + a_2 + \ldots + a_{80090} )^2 + a_1 ^2 + a_2^2 + \ldots + a_{80090}^2 \leq 80090. \]
What is the smallest integer value of \(N\) such that for all possible such tuples \((a_1,...,a_{80090})\), we have \( |a_i| \leq N \) for all \(i\)?
by
Calvin Lin