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Does it continue? An original. (Posted on 2017-10-20) Difficulty: 3 of 5

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.

No Solution Yet Submitted by Jer    
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re(3): computer solution Comment 7 of 7 |
(In reply to re(2): computer solution by chun)

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

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