TITLE: Finding the number of divisors of a number?
QUESTION [7 upvotes]: How can I find the number of divisors of $2011\times2012\times2013\times2014+1$?

REPLY [6 votes]: Hint $\ \ \ \overbrace{n(n+3)}^{\Large\ \ x_{\phantom{I_i}}}\ \overbrace{(n+1)(n+2)}^{\Large (x+2)} + 1\, =\, x(x+2)+1\, =\, (x+1)^2 =\, (n^2+3n+1)^2$