Let ... be a seqence of positive integers for which

Prove that and are relatively prime for every nonnegative integer .

...

...

...

There doesn't seem to be a discernable pattern, but any how, I think these can be approached by Strong Induction.

The basis case is easy. is obvious.

The Inductive step: Assume . We show that ,

I can't see the recurrence relation for . Need help.