AUSTRIAN-POLISH 2004 Problem 8

a.) Prove that for $n = 4$ or $n \geq 6$ each triangle $ABC$ can be decomposed in $n$ similar (not necessarily congruent) triangles.

b.) Show: An equilateral triangle can neither be composed in 3 nor 5 triangles.

c.) Is there a triangle $ABC$ which can be decomposed in 3 and 5 triangles, analogously to a.). Either give an example or prove that there is not such a triangle.