19. Two natural numbers both give a remainder of 2 when divided by 3. What remainder does their product give when divided by 3?
19. $(3 m+2)(3 n+2)=3(m n+m+n+1)+1$.

Translating the above text into English, while preserving the original text's line breaks and format, results in:

19. $(3 m+2)(3 n+2)=3(m n+m+n+1)+1$.