If you take the product of any four consecutive integers and then add one, the result
is always a perfect square!
 Example 1:

1*2*3*4 + 1 = 25 = 5^{2}
 Example 2:

2*3*4*5 + 1 = 121 = 11^{2}
 Example 3:

3*4*5*6 + 1 = 361 = 19^{2}
 Why does this work?

n(n+1)(n+2)(n+3) + 1 = n^{4} + 6n^{3} + 11n^{2} + 6n + 1
= (n^{2} + 3n + 1)^{2}.
