MathNet 2008-part-03 — 165 problems (EN–VI) Question 24

Let $n$ be a positive integer. Does $(2n-3)(2n-1)(2n+1)(2n+3)+16$ equal the square of a positive integer? Does the number $2005 \times 2007 \times 2009 \times 2011 + 16$ equal the square of a positive integer?