4. In a right-angled triangle, the lengths of all sides are natural numbers, with one of the legs equal to 2012.

a) (7th grade) Find at least one such triangle.

b) (8th-9th grades) Find all such triangles. Answer: b) $(2012,253005,253013); (2012,506016, 506020); (2012,1012035,1012037)$ and $(2012,1509,2515)$.