How do I properly decrypt RSA knowing all the parameters?

[Owltooth]

Select Topic Area

Question

Body

Sorry if wrong category. My first time using these.
I've spent all night trying to write the RSA algorithm and it's fine. It works. It encrypts and decrypts.
But the decryption is WAAAY too slow because 99999^999999 is too much even for computers to handle.
I've read about RSA on wiki (https://en.wikipedia.org/wiki/RSA_(cryptosystem)) and it says that I could use the Chinese remainder theorem (https://en.wikipedia.org/wiki/Chinese_remainder_theorem) by decrypting the encrypted message in two parts and then merging them. The problem is I don't understand how to merge m1 and m2 into the original m at all. How do I do that? Thank you in advance.

[Owltooth]

This is kind of unreadable

[Owltooth]

I also tried that earlier but I couldn't understand how 13^(-1) mod 11 = 6

[Owltooth]

https://stackoverflow.com/questions/21118202/how-would-i-implement-an-efficient-powers-method-in-java