Why would you want a- b or a+ b to be a multiple of 99? The left side is not likely to be!

The right side is , a difference of squares.

Neither 1 nor 2 is a difference of squares but 3 is: you could have x= 3(99)= 297, a= 2, b= 1. 4 is not a difference of squares but 5 is: you could have x= 5(99)= 495, a= 3, b= 2.

Am I misunderstanding your question?