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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(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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