In the above examples, the number that must be added to each factorial to reach the first perfect square beyond it is itself a perfect square. (With the exception of 2! and 3!)

Make a conjecture about whether the observed pattern continues before you try to prove it or find a counterexample.

I realized as Chun did that every factorial could yield a square by adding another square.  What I thought was curious was that they seemed so close to a square.  The first few squares that must be added are of 1, 1, 3, 1, 9 and although they tend to grow they don't seem to grow very fast. 

Posted by Jer on 2017-10-20 15:52:46