Suppose we have a sequence a_{1}, a_{2}, \ldots of positive real numbers so that for each positive integer n, we have that \sum_{k=1}^{n} a_{k} a_{\lfloor\sqrt{k}\rfloor}=n^{2}. Determine the first value of k so a_{k}>100.
Suppose we have a sequence a_{1}, a_{2}, \ldots of positive real numbers so that for each positive integer n, we have that \sum_{k=1}^{n} a_{k} a_{\lfloor\sqrt{k}\rfloor}=n^{2}. Determine the first value of k so a_{k}>100.