Question 6
For each positive integer $n$, denote by $s(n)$ the greatest integer such that for all positive integer $k\le s(n)$, $n^2$ can be expressed as a sum of squares of $k$ positive integers.
(a) Prove that $s(n)\le n^2-14$ for all $n\ge4$.
(b) Find a number $n$ such that $s(n)=n^2-14$.
(c) Prove that there exist infinitely many positive integers $n$ such that $s(n)=n^2-14$.
(a) Prove that $s(n)\le n^2-14$ for all $n\ge4$.
(b) Find a number $n$ such that $s(n)=n^2-14$.
(c) Prove that there exist infinitely many positive integers $n$ such that $s(n)=n^2-14$.