Find the smallest positive integer N such that each of the 101 intervals
\left[N^{2},(N+1)^{2}\right),\left[(N+1)^{2},(N+2)^{2}\right), \cdots,\left[(N+100)^{2},(N+101)^{2}\right)
contains at least one multiple of 1001.
Find the smallest positive integer N such that each of the 101 intervals
contains at least one multiple of 1001.