We do give a shit, just not always have any insight to share. I've found that for e=0 you can get to all records where a and b are a multiple of n just by starting at (0, n, 1) and jumping by t = t + n. First image is using c6107's d value of 78 to get to (0, 78, 1), and then jumping.
Somehow this works for 2d as well, where jumping by t+78 from (0, 156, 1), the a and b values are still always divisible by 78. Next level up you could use 156 * 2 = 312 and go to (0, 312, 1+312), and a and b is always divisible by 156.
This diagonal movement increases c 4 times for each step, and has some really interesting patterns in the generated records, not sure what to make of them yet