Problem 1: Pairs of Squares

1729 is the smallest number that can be expressed as the sum of a pair of (positive) cubes in two different ways: 1729=13+123=93+103

  1. What is the smallest number that can be expressed as the sum of a pair of positive squares in two different ways?
  2. What is the smallest number that can be expressed as the sum of a pair of distinct positive squares in two different ways?
  3. (Harder) And now for something with a difference. How many pairs of squares have a difference of 1729?‌