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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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 A Counterexample | Comment 1 of 7

12! = 479001600

square root of 479001600 is 21886.105

21887^2 = 479040769

479040769 - 479001600 = 39169, which is not a perfect square.

 Posted by chun on 2017-10-20 08:09:12
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