I think the most common is “X is left as an exercise for the reader”, but it looks like both are in use.
Is the “to” variant correct? If not, why?
I would say the alternatives should be:
- Left to the reader as an exercise
- Left as an exercise for the reader
It seems to me that “to the reader” modifies “left” whereas “for the reader” could modify left or it could modify exercise. When left at the end as in the question, then I’d have to suggest that “to the reader” is incorrect.