The existence of cyclic numbers is made clear by the simultaneous linear equations. It was proven that for 3 digit numbers 495 is a unique cyclic number and likewise 6174 for 4 digit numbers. It was also confirmed that all 3 digit numbers converge on 495 and that all 4 digit numbers converge on 6174. However, this was merely demonstrated, and I think that the real reason why all the numbers converge on the cyclic number has not been demonstrated