Wednesday, January 14, 2009

2009

Since we are at the beginning of 2009, I will try to break the ice with a list of problems involving the number 2009.
  1. Factor 2009.
  2. Write 2009 as a sum of two squares: 2009=x^2+y^2 with integers x and y.
  3. If x and y are integers and if x^2+y^2 is a multiple of 2009, is it true that both x and y must be multiples of 7?
  4. How many zeros are there at the end of 2009! ?