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## Main Question or Discussion Point

I wish to show that the sum of 9 consecutive natural numbers: n(n+1)(n+2)(n+3)...(n+8) will not be a perfect square.

This problem came by as a result of another problem I was doing and I'm wondering if anyone knows/has come across this already.

After some searching I found that n! is not a perfect square (although I found no proof).

In my case I wish to show that (n+8)!-(n-1)! is not a perfect square.

This problem came by as a result of another problem I was doing and I'm wondering if anyone knows/has come across this already.

After some searching I found that n! is not a perfect square (although I found no proof).

In my case I wish to show that (n+8)!-(n-1)! is not a perfect square.