2nd Swedish Mathematical Society Problems 1962

1.  Find all polynomials f(x) such that f(2x) = f '(x) f ''(x). 2.  ABCD is a square side 1. P and Q lie on the side AB and R lies on the side CD. What are the possible values for the circumradius of PQR? 3.  Find all pairs (m, n) of integers such that n2 - 3mn + m - n = 0.