26th British Mathematical Olympiad 1990 Problems

26th British Mathematical Olympiad 1990 Problems1.  Show that if a polynomial with integer coefficients takes the value 1990 at four different integers, then it cannot take the value 1997 at any integer. 2.  The fractional part { x } of a real number is defined as x - [x]. Find a positive real x such that { x } + { 1/x } = 1 (*). Is there a rational x satisfying