I am trying to understand how this method for simplifying the decryption process works. I understand that if I have the message c raised to the public exponent modulo the modulus, then to decrypt it, I need to raise the encrypted message to the private exponent modulo the modulus.

Say I have a public key (13, 673627) and a private key (103381, 673627) and I want to read the message 174277, I understand that I can do this by raising and taking mod 673627 to get it. However, I have a guided question that goes through a method that doesn't require as much computation and I don't quite understand it.

It says "find the other information in (103381, 673627), is chosen so that , chosen so that and chosen so that .

I factored the modulus to get 673627 = 919*733 =

I found that:

and

and

How do I use them to decrypt 174277?