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Real numbers a1,a2,…,a80090 a_1, a_2, \ldots, a_{80090} a1,a2,…,a80090 satisfy
(a1+a2+…+a80090)2+a12+a22+…+a800902≤80090. (a_1 + a_2 + \ldots + a_{80090} )^2 + a_1 ^2 + a_2^2 + \ldots + a_{80090}^2 \leq 80090. (a1+a2+…+a80090)2+a12+a22+…+a800902≤80090.
What is the smallest integer value of NNN such that for all possible such tuples (a1,...,a80090)(a_1,...,a_{80090})(a1,...,a80090), we have ∣ai∣≤N |a_i| \leq N ∣ai∣≤N for all iii?
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