I was watching a video recently, and I saw how 10*9*8*7 was equal to 7*6*5*4*3*2*1, or to make it clearer, 10!/6!=7!. I was wondering if there were any other solutions, so I checked the web, to find nothing. I also checked Wolfram alpha, but it gave me just two extra solutions for x=10 and point.
So, what kind of solutions are there? Are there infinite solutions for any arbitrary x? Are there infinite integer solutions for x and y?
Anything would help, I have no idea of how to find these kinds of solutions...
EDIT: Thomas Andrews told me that when talking about negative integers I should use the Gamma function. But to make it simple, can you simply extend the question to negative or complex numbers? Thanks.