53rd Polish Mathematical Olympiad Problems 2002

53rd Polish Mathematical Olympiad Problems 2002A1.  Find all triples of positive integers (a, b, c) such that a2 + 1 and b2 + 1 are prime and (a2 + 1)(b2 + 1) = c2 + 1. A2.  ABC is an acute-angled triangle. BCKL, ACPQ are rectangles on the outside of two of the sides and have equal area. Show that the midpoint of PK lies on the line through C and the circumcenter.

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