What are the possible solutions for the equation a!b! = a! + b! + c! ?

[Mattofix]

Homework Statement

Just a quick on - this is a little bit out of a bigger question.

Does ( 2(n+1))! = 2!(n+1)! ) ?

Do you know of anywhere on the net where i can find factorial properties?

Thanks

 

[scottie_000]

Homework Statement

Does ( 2(n+1))! = 2!(n+1)! ) ?

Do you know of anywhere on the net where i can find factorial properties?

Thanks

No they are not equal.
If you write out those factorials explicitly you should see why
See http://en.wikipedia.org/wiki/Factorials" if you want more info

 

[HallsofIvy]

Did you TRY anything at all? If n= 1, (2(n+1))!= (2(2))!= 4!= 24 while 2!(n+1)! = 2(2)= 4. You can't get simpler than that.

 

[Mattofix]

yeah - i did after i posted - too hasty - sorry

 

[Mattofix]

so I am meant to calcultae the radius of convergence and i have got to

... lZl(2(n+1))!/(2n)!(n+1)^2what shall i do with the (2(n+1))!/(2n)! ?

 

[HallsofIvy]

(2n)!= (2n)(2n-1)... (n+1)! so 2(n+1)!/(2n)!= 2/[(2n)(2n-1)...(n+2)!]. what happens to that as n goes to infinity?

 

[xsm113r]

Hi, similar kind of question.

Find all solutions in positive integers a; b; c to the equation
a!b! = a! + b! + c!

I have rearranged and got (a!-1)(b!-1) = c!+1

And the only solutions I can find are a=3 b=3 c=4 but I can't be sure that they are the only ones. How would I go about finding other solutions?