10th Swedish Mathematical Society Problems 1970

1.  Show that infinitely many positive integers cannot be written as a sum of three fourth powers of integers. 2.  6 open disks in the plane are such that the center of no disk lies inside another. Show that no point lies inside all 6 disks.3.  A polynomial with integer coefficients takes the value 5 at five distinct integers. Show that it does not take the value 9