Hi I haven't had any luck with these questions. Any hints on them:

1. Can 1000003 be written as the sum of 2 square numbers?

2. Prove that 801,279,386,104 can't be written as the sum of 3 cubes

3. There is a set of numbers whose sum is equal to the sum of the elements squared. What's bigger: the sum of the cubes or the sum of the fourth powers?