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 Does it continue? An original. (Posted on 2017-10-20)
2!+2=4=22
3!+3=9=32
4!+1=25=52
5!+1=121=112
6!+9=729=272
7!+1=5041=712
8!+81=40401=2012

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 No Rating

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 re: computer solution | Comment 3 of 7 |
(In reply to computer solution by Charlie)

Note: with 12! if instead of going to the next square, you go instead to the one after that, the difference is a perfect square.

21888^2-12!=82944=288^2

I haven't looked into 17! and above.

 Posted by Jer on 2017-10-20 11:12:26

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