Did You Know?

by Herb Conn in Recreational & Educational Computing

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 = 52

Example 2:

2*3*4*5 + 1 = 121 = 112

Example 3:

3*4*5*6 + 1 = 361 = 192

Why does this work?

n(n+1)(n+2)(n+3) + 1 = n4 + 6n3 + 11n2 + 6n + 1 = (n2 + 3n + 1)2.