Hypatia was an Egyptian female mathematician born in A.D. 370. One problem she posed was the following:

  • Find a number that is the sum of two squares and whose square is also the sum of two squares.
  • Can you solve Hypatia’s problem? Are there more solutions? Is there a pattern between any pair of solutions?

Justify your answers.

(Source: Mathematics Teaching in the Middle School, Apr 1994)