MHB What are the ordered pairs for (1+a!)(1+b!) = (a+b)!?

[juantheron]

Find all ordered pairs $(a,b)$ for which $(1+a!)(1+b!) = (a+b)!$

where $a,b\in \mathbb{N}$ and $n! = $ factorial on $n$

 

[mente oscura]

Find all ordered pairs $(a,b)$ for which $(1+a!)(1+b!) = (a+b)!$

where $a,b\in \mathbb{N}$ and $n! = $ factorial on $n$

Hello.

Spoiler

http://mathhelpboards.com/challenge-questions-puzzles-28/solving-equation-ii-9685.html

Regards.