Properties of a general knight in the knight's tour problem.

Question

I am currently investigating how the knight's tour problem differs when a general knight (m, n) is used instead of a traditional knight (2, 1), where m represents moving a number of squares along one axis and n represents the number of squares along the other. Right now I am just approaching this problem through simply examining various examples and it's more of a trial and error basis. I am trying to determine the similarities and differences between the two problems. I think there might be a more structured approach to this and if anyone could provide some insight it would be greatly appreciated. I have limited experience with programming which is something I have attempted to work with so if there are any experienced programmers here that could give me advice on how to approach this problem that would be great as well :)