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IMO LongList 1987 - Cover a rectangle with triminos

Source:

September 6, 2010
geometryrectanglecombinatorics unsolvedcombinatorics

Problem Statement

Is it possible to cover a rectangle of dimensions m×nm \times n with bricks that have the trimino angular shape (an arrangement of three unit squares forming the letter L\text L) if:
(a) m×n=1985×1987;m \times n = 1985 \times 1987;
(b) m \times n = 1987 \times 1989   ?
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