There are 300 followers. Yay!
Algebra
Level
5
Consider all \(n\)-tuples of real numbers, \(\displaystyle{(x_{1}, x_{2}, x_{3}, ..., x_{n})}\) such that \(\displaystyle{\sum_{i=1}^n x_{i}^{2} =1}\) where \(n\) is a positive integer.
Let \(M_{n}\) be the maximum value of \(\displaystyle{\sum_{i=1}^n i x_{i}}\) over all such \(n\)-tuples.
Determine the sum of all integers \(\displaystyle{p, 1 \leq p \leq 300}\) such that \(M_{p}\) is an integer.
by
Joel Tan