## anonymous 4 years ago a!+b! = a^b

1. anonymous

I can be rewritten using the gamma function as: $\Gamma(a+1) + \Gamma(b+1) = a^{b}$

2. anonymous

Any idea how to solve this?

3. anonymous

As you might know this is my problem which I posted here http://math.stackexchange.com/questions/105923/

4. anonymous

I have a feeling that the proving that only (2,2) and (2,3) are the only solutions is somewhat difficult.

5. anonymous

Try using the gamma function.

6. anonymous

So you have a solution Aron?

7. AravindG

nic question aron

8. anonymous

No,I don't have a solution but I was just wondering if I could solve it using the gamma function.

9. anonymous

10. anonymous

$\Gamma (Z) = \int\limits\limits_{0}^{\infty}e^{-t}t^{z-1}dt$

11. anonymous

$$\stackrel{\circ.\circ}{\huge o}\angle\huge\lbrace\normalsize\text{I am tired, time for a nap! }$$

12. anonymous

Is there a way to format text in the math formatter so it isn't italicized?

13. anonymous

\text{}

14. anonymous

The graph looks weird!

15. anonymous
16. anonymous

It looks like an alien spaceship

17. anonymous

haha :D

18. anonymous

yeah

19. anonymous

Anyone able to solve it yet?

20. precal

Cool graph! You guys are so funny!