**2**=4=2

^{2}

3!+

**3**=9=3

^{2}

4!+

**1**=25=5

^{2}

5!+

**1**=121=11

^{2}

6!+

**9**=729=27

^{2}

7!+

**1**=5041=71

^{2}

8!+

**81**=40401=201

^{2}

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.