Is there a method to make a rep-n rep-tile for any number n, using only triangles? And if there is no such method, what's the smallest number for which there's no example? I'm only considering rep-tiles which are all of the same size, as they make up the larger congruent rep-tile.

I first asked the more general question, can you do it for any shape, not just triangles? But then I felt confident that you can do it with rectangles, for any n.